The cl-mathstats Reference Manual

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The cl-mathstats Reference Manual

This is the cl-mathstats Reference Manual, version 0.8.2, generated automatically by Declt version 2.3 "Robert April" on Tue Jan 09 13:49:12 2018 GMT+0.


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1 Systems

The main system appears first, followed by any subsystem dependency.


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1.1 cl-mathstats

Maintainer

Gary Warren King <gwking@metabang.com>

Author

Gary Warren King <gwking@metabang.com>

License

MIT Style License

Description

Common Lisp math and statistics routines

Version

0.8.2

Dependencies
Source

cl-mathstats.asd (file)

Components

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2 Modules

Modules are listed depth-first from the system components tree.


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2.1 cl-mathstats/dev

Parent

cl-mathstats (system)

Location

dev/

Components

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2.2 cl-mathstats/website

Parent

cl-mathstats (system)

Location

/home/quickbuilder/quicklisp/dists/quicklisp/software/cl-mathstats-20140713-git/website/ (not found)

Component

source (module)


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2.3 cl-mathstats/website/source

Parent

website (module)

Location

/home/quickbuilder/quicklisp/dists/quicklisp/software/cl-mathstats-20140713-git/website/source/ (not found)

Component

index.md (file)


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3 Files

Files are sorted by type and then listed depth-first from the systems components trees.


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3.1 Lisp


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3.1.1 cl-mathstats.asd

Location

cl-mathstats.asd

Systems

cl-mathstats (system)

Packages

asdf-cl-mathstats


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3.1.2 cl-mathstats/dev/package.lisp

Parent

dev (module)

Location

dev/package.lisp

Packages

cl-mathstats


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3.1.3 cl-mathstats/dev/api.lisp

Dependency

package.lisp (file)

Parent

dev (module)

Location

dev/api.lisp

Exported Definitions

dot-product (generic function)


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3.1.4 cl-mathstats/dev/parameters.lisp

Dependency

package.lisp (file)

Parent

dev (module)

Location

dev/parameters.lisp

Internal Definitions

*gaussian-cdf-signals-zero-standard-deviation-error* (special variable)


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3.1.5 cl-mathstats/dev/math-utilities.lisp

Dependency

package.lisp (file)

Parent

dev (module)

Location

dev/math-utilities.lisp

Exported Definitions

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3.1.6 cl-mathstats/dev/class-defs.lisp

Dependency

package.lisp (file)

Parent

dev (module)

Location

dev/class-defs.lisp

Internal Definitions

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3.1.7 cl-mathstats/dev/definitions.lisp

Dependency

math-utilities.lisp (file)

Parent

dev (module)

Location

dev/definitions.lisp

Exported Definitions

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3.1.8 cl-mathstats/dev/binary-math.lisp

Dependency

package.lisp (file)

Parent

dev (module)

Location

dev/binary-math.lisp

Exported Definitions

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3.1.9 cl-mathstats/dev/matrices.lisp

Dependency

package.lisp (file)

Parent

dev (module)

Location

dev/matrices.lisp

Exported Definitions
Internal Definitions

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3.1.10 cl-mathstats/dev/matrix-fns.lisp

Dependency

matrices.lisp (file)

Parent

dev (module)

Location

dev/matrix-fns.lisp

Exported Definitions
Internal Definitions

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3.1.11 cl-mathstats/dev/density-fns.lisp

Dependency

parameters.lisp (file)

Parent

dev (module)

Location

dev/density-fns.lisp

Exported Definitions
Internal Definitions

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3.1.12 cl-mathstats/dev/svd.lisp

Dependency

matrix-fns.lisp (file)

Parent

dev (module)

Location

dev/svd.lisp

Internal Definitions

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3.1.13 cl-mathstats/dev/utilities.lisp

Dependency

package.lisp (file)

Parent

dev (module)

Location

dev/utilities.lisp

Exported Definitions
Internal Definitions

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3.1.14 cl-mathstats/dev/define-statistical-fun.lisp

Dependency

package.lisp (file)

Parent

dev (module)

Location

dev/define-statistical-fun.lisp

Exported Definitions

convert (method)

Internal Definitions

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3.1.15 cl-mathstats/dev/basic-statistics.lisp

Dependencies
Parent

dev (module)

Location

dev/basic-statistics.lisp

Exported Definitions
Internal Definitions

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3.1.16 cl-mathstats/dev/smoothing.lisp

Dependency

utilities.lisp (file)

Parent

dev (module)

Location

dev/smoothing.lisp

Exported Definitions

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3.1.17 cl-mathstats/dev/correlation-regression.lisp

Dependencies
Parent

dev (module)

Location

dev/correlation-regression.lisp

Exported Definitions
Internal Definitions

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3.1.18 cl-mathstats/dev/anova.lisp

Dependency

package.lisp (file)

Parent

dev (module)

Location

dev/anova.lisp

Exported Definitions
Internal Definitions

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3.2 Other


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3.2.1 cl-mathstats/website/source/index.md

Parent

source (module)

Location

/home/quickbuilder/quicklisp/dists/quicklisp/software/cl-mathstats-20140713-git/website/source/index.md (not found)


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4 Packages

Packages are listed by definition order.


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4.1 asdf-cl-mathstats

Source

cl-mathstats.asd

Use List

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4.2 cl-mathstats

Source

package.lisp (file)

Nickname

metabang.math

Use List
Exported Definitions
Internal Definitions

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5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.


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5.1 Exported definitions


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5.1.1 Constants

Constant: +0degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +10degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +120degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +135degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +150degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +15degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +180degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +210degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +225degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +240degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +270degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +300degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +30degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +315degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +330degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +360degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +45degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +5degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +60degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +90degrees+
Package

cl-mathstats

Source

definitions.lisp (file)

Constant: +e+

An approximation of the constant e (named for Euler!).

Package

cl-mathstats

Source

math-utilities.lisp (file)

Constant: 2fpi

The constant 2*pi, in single-float format. Using this constant avoid run-time double-float contagion.

Package

cl-mathstats

Source

math-utilities.lisp (file)

Constant: fpi

The constant pi, in single-float format. Using this constant avoid run-time double-float contagion.

Package

cl-mathstats

Source

math-utilities.lisp (file)


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5.1.2 Macros

Macro: underflow-goes-to-zero &body BODY

Protects against floating point underflow errors and sets the value to 0.0 instead.

Package

cl-mathstats

Source

density-fns.lisp (file)

Macro: with-temp-table (TEMP) &body FORMS

Binds ‘temp’ to a hash table.

Package

cl-mathstats

Source

utilities.lisp (file)

Macro: with-temp-vector (TEMP MIN-SIZE) &body FORMS

Binds ‘temp’ to a vector of length at least ‘min-size.’ It’s a vector of pointers and has a fill-pointer, initialized to ‘min-size.’

Package

cl-mathstats

Source

utilities.lisp (file)


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5.1.3 Functions

Function: anova-one-way-variables &rest ARGS

ANOVA-ONE-WAY-VARIABLES (IV DV &OPTIONAL (SCHEFFE-TESTS-P T) CONFIDENCE-INTERVALS)
Performs a one-way analysis of variance (ANOVA) on the input data, which should be two equal-length sequences: ‘iv’ is the independent variable, represented as a sequence of categories or group identifiers, and ‘dv’ is the dependent variable, represented as a sequence of numbers. The ‘iv’ variable must be “sorted,” meaning that AAABBCCCCCDDDD is okay but ABCDABCDABDCDC is not, where A, B, C and D are group identifiers. Furthermore, each group should consist of at least 2 elements.

The significance of the result indicates that the group means are not all equal; that is, at least two of the groups have significantly different means. If there were only two groups, this would be semantically equivalent to an unmatched, two-tailed t-test, so you can think of the one-way ANOVA as a multi-group, two-tailed t-test.

This function returns five values: 1. an ANOVA table; 2. a list a group means; 3. either a Scheffe table or nil depending on ‘scheffe-tests-p’; and 4. an alternate value for SST. 5. a list of confidence intervals in the form ‘(,mean ,lower ,upper) for each group, if ‘confidence-intervals’ is a number between zero and one, giving the kind of confidence interval, such as 0.9. The fourth value is only interesting if you think there are numerical accuracy problems; it should be approximately equal to the SST value in the ANOVA table. This function differs from ‘anova-one-way-groups’ only in its input representation. See the manual for more information.

Package

cl-mathstats

Source

anova.lisp (file)

Function: anova-two-way-variables &rest ARGS

ANOVA-TWO-WAY-VARIABLES (DV IV1 IV2)
Calculates the analysis of variance when there are two factors that may affect the dependent variable, specifically ‘iv1’ and ‘iv2.’ Unlike the one-way ANOVA, there are mathematical difficulties with the two-way ANOVA if there are unequal cell sizes; therefore, we require all cells to be the same size; that is, the same number of values (of the dependent variable) for each combination of the independent factors.

The result of the analysis is an anova-table, as described in the manual. This function differs from ‘anova-two-way-groups’ only in its input representation. See the manual for further discussion of analysis of variance.
The row effect is ‘iv1’ and the column effect is ‘iv2.’

Package

cl-mathstats

Source

anova.lisp (file)

Function: anova-two-way-variables-unequal-cell-sizes &rest ARGS

ANOVA-TWO-WAY-VARIABLES-UNEQUAL-CELL-SIZES (IV1 IV2 DV)
Calculates the analysis of variance when there are two factors that may affect the dependent variable, specifically ‘iv1’ and ‘iv2.’

Unlike the one-way ANOVA, there are mathematical difficulties with the two-way ANOVA if there are unequal cell sizes. This function differs fron the standard two-anova by (1) the use of cell means as single scores, (2) the division of squared quantities by the number of cell means contributing to the quantity that is squared and (3) the multiplication of a "sum of squares" by the harmonic mean of the sample sizes.

The result of the analysis is an anova-table, as described in the manual. See the manual for further discussion of analysis of
variance. The row effect is ‘iv1’ and the
column effect is ‘iv2.’

Package

cl-mathstats

Source

anova.lisp (file)

Function: autocorrelation &rest ARGS

AUTOCORRELATION (SAMPLE MAX-LAG &OPTIONAL (MIN-LAG 0))
Autocorrelation is merely a cross-correlation between a sample and itself. This function returns a list of correlations, where the i’th element is the correlation of the sample with the sample starting at ‘i.’

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: beta Z W

Returns the value of the Beta function, defined in terms of the complete gamma function, G, as: G(z)G(w)/G(z+w). The implementation follows Numerical Recipes in C, section 6.1.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: beta-incomplete A B X

This function is useful in defining the cumulative distributions for Student’s t and the F distribution.

All arguments must be floating-point numbers; ‘a’ and ‘b’ must be positive and ‘x’ must be between 0.0 and 1.0, inclusive.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: binomial-cdf P N K

Suppose an event occurs with probability ‘p’ per trial. This function computes the probability of ‘k’ or more events occurring in ‘n’ trials. Note that this is the complement of the usual definition of cdf. This function approximates the actual computation using the incomplete beta function, but is preferable for large ‘n’ (greater than a dozen or so) because it avoids summing many tiny floating-point numbers.

The implementation follows Numerical Recipes in C, section 6.3
.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: binomial-cdf-exact P N K

This is an exact but computationally intensive form of the preferred function, ‘binomial-cdf.’

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: binomial-coefficient N K

Returns the binomial coefficient, ‘n’ choose ‘k,’ as an integer. The result may not be exactly correct, since the computation is done with logarithms. The result is rounded to an integer. The implementation follows Numerical Recipes in C, section 6.1

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: binomial-coefficient-exact N K

This is an exact but computationally intensive form of the preferred function, ‘binomial-coefficient.’

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: binomial-probability P N K

Returns the probability of ‘k’ successes in ‘n’ trials, where at each trial the probability of success is ‘p.’ This function uses floating-point approximations, and so is computationally efficient but not necessarily exact.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: binomial-probability-exact P N K

This is an exact but computationally intensive form of the preferred function, ‘binomial-probability.’

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: chi-square-significance X DOF

Computes the complement of the cumulative distribution function for a Chi-square random variable with ‘dof’ degrees of freedom evaluated at ‘x.’ The result is the probability that the observed chi-square for a correct model should be greater than ‘x.’ The implementation follows Numerical Recipes in C, section 6.2. Small values suggest that the null hypothesis should be rejected; in other words, this computes the significance of ‘x.’

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: combination-count N K

Returns the number of combinations of n elements taken k at a time. Assumes valid input.

Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: confidence-interval &rest ARGS

CONFIDENCE-INTERVAL NIL NIL

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: confidence-interval-proportion &rest ARGS

CONFIDENCE-INTERVAL-PROPORTION (X N CONFIDENCE)
Suppose we have a sample of ‘n’ things and ‘x’ of them are “successes.” We can estimate the population proportion of successes as x/n; call it ‘p-hat.’ This function computes the estimate and a confidence interval on it. This function is not appropriate for small samples with p-hat far from 1/2: ‘x’ should be at least 5, and so should ‘n’-‘x.’ This function returns three values: p-hat, and the lower and upper bounds of the confidence interval. ‘Confidence’ should be a number between 0 and 1, exclusive.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: confidence-interval-t &rest ARGS

CONFIDENCE-INTERVAL-T (DATA CONFIDENCE)
Suppose you have a sample of 10 numbers and you want to compute a 90 percent confidence interval on the population mean. This function is the one to use. This function uses the t-distribution, and so it is appropriate for small sample sizes. It can also be used for large sample sizes, but the function ‘confidence-interval-z’ may be computationally faster. It returns three values: the mean and the lower and upper bound of the confidence interval. True, only two numbers are necessary, but the confidence intervals of other statistics may be asymmetrical and these values would be consistent with those confidence intervals. ‘Sample’ should be a sequence of numbers. ‘Confidence’ should be a number between 0 and 1, exclusive.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: confidence-interval-t-summaries MEAN DOF STANDARD-ERROR CONFIDENCE

This function is just like ‘confidence-interval-t,’ except that instead of its arguments being the actual data, it takes the following summary statistics: ‘mean,’ which is the estimator of some t-distributed parameter; ‘dof,’ which is the number of degrees of freedom in estimating the mean; and the ‘standard-error’ of the estimator. In general, ‘mean’ is a point estimator of the mean of a t-distribution, which may be the slope parameter of a regression, the difference between two means, or other practical t-distributions. ‘Confidence’ should be a number between 0 and 1, exclusive.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: confidence-interval-z &rest ARGS

CONFIDENCE-INTERVAL-Z (DATA CONFIDENCE)
Suppose you have a sample of 50 numbers and you want to compute a 90 percent confidence interval on the population mean. This function is the one to use. Note that it makes the assumption that the sampling distribution is normal, so it’s inappropriate for small sample sizes. Use confidence-interval-t instead. It returns three values: the mean and the lower and upper bound of the confidence interval. True, only two numbers are necessary, but the confidence intervals of other statistics may be asymmetrical and these values would be consistent with those confidence intervals. This function handles 90, 95 and 99 percent confidence intervals as special cases, so those will be quite fast. ‘Sample’ should be a sequence of numbers. ‘Confidence’ should be a number between 0 and 1, exclusive.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: correlation &rest ARGS

CORRELATION (SAMPLE1 SAMPLE2 &KEY START1 END1 START2 END2) Computes the correlation coefficient of two samples, which should be equal-length sequences of numbers.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: correlation-from-summaries N X X2 Y Y2 XY

Computes the correlation of two variables given summary statistics of the variables. All of these arguments are summed over the variable: ‘x’ is the sum of the x’s, ‘x2’ is the sum of the squares of the x’s, and ‘xy’ is the sum of the cross-products, which is also known as the inner product of the variables x and y. Of course, ‘n’ is the number of data values in each variable.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: correlation-matrix DV IVS

Returns a matrix of all the correlations of all the variables. The dependent variable is row and column zero.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: covariance &rest ARGS

COVARIANCE (SAMPLE1 SAMPLE2 &KEY START1 END1 START2 END2)
Computes the covariance of two samples, which should be equal-length sequences of numbers. Covariance is the inner product of differences between sample elements and their sample means. For more information, see the manual.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: cross-correlation &rest ARGS

CROSS-CORRELATION (SEQUENCE1 SEQUENCE2 MAX-LAG &OPTIONAL (MIN-LAG 0)) Returns a list of the correlation coefficients for all lags from ‘min-lag’ to ‘max-lag,’ inclusive, where the ‘i’th list element is the correlation of the first (length-of-sequence1 - i) elements of sequence1 with with the last i elements of sequence2. Both sequences should be sequences of numbers and of equal length.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: d-test &rest ARGS

D-TEST (SAMPLE-1 SAMPLE-2 TAILS &KEY (TIMES 1000) (H0MEAN 0))
Two-sample test for difference in means. Competes with the unmatched, two-sample t-test. Each sample should be a sequence of numbers. We calculate the mean of ‘sample-1’ minus the mean of ‘sample-2’; call that D. Under the null hypothesis, D is zero. There are three possible alternative hypotheses: D is positive, D is negative, and D is either, and they are selected by the ‘tails’ parameter, which must be :positive, :negative, or :both, respectively. We count the number of chance occurrences of D in the desired rejection region, and return the estimated probability.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: data-length &rest ARGS

DATA-LENGTH (DATA &KEY START END KEY)
Returns the number of data values in ‘data.’ Essentially, this is the Common Lisp ‘length’ function, except it handles sequences where there is a ‘start’ or ‘end’ parameter. The ‘key’ parameter is ignored.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: degrees->radians DEGREES

Convert degrees to radians.

Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: div2 I &optional POWER

Divide positive fixnum ‘i’ by 2 or a power of 2, yielding an integer result. For example, (div2 35 5) => 1.

Package

cl-mathstats

Source

binary-math.lisp (file)

Function: ensure-float NUMBER
Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: error-function X

Computes the error function, which is typically used to compute areas under the Gaussian probability distribution. See the manual for more information. Also see the function ‘gaussian-cdf.’

This implementation follows Numerical Recipes in C, section 6.2

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: error-function-complement X

This function computes the complement of the error function, “erfc(x),” defined as 1-erf(x). See the documentation for ‘error-function’ for a more complete definition and description. Essentially, this function on z/sqrt2 returns the two-tailed significance of z in a standard Gaussian distribution.

This function implements the function that Numerical Recipes in C calls erfcc, see section 6.3; that is, it’s the one using the Chebyshev approximation, since that is the one they call from their statistical functions. It is quick to compute and has fractional error everywhere less than 1.2x10^\{-7\}.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: exp2 N

2^n

Package

cl-mathstats

Source

binary-math.lisp (file)

Function: extract-unique-values SEQUENCE

A faster version of ‘remove-duplicates’. Note you cannot specify a :TEST (it is always #’eq).

Package

cl-mathstats

Source

utilities.lisp (file)

Function: f-measure PRECISION RECALL &optional BETA

Returns the f-measure, the combination of precision and recall based on parameter beta - default = .5 which => precision and recall are equally weighted. beta = 1 => precision is maximized. beta = 0 => recall is maximized.

From a recent statistics book - All of Statistics - springer verlag http://www2.springeronline.com/sgw/cda/frontpage/0,,4-10128-22-13887455-0,00.html

Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: f-significance F-STATISTIC NUMERATOR-DOF DENOMINATOR-DOF &optional ONE-TAILED-P

This function occurs in the statistical test of whether two observed samples have the same variance. A certain statistic, F, essentially the ratio of the observed dispersion of the first sample to that of the second one, is calculated. This function computes the tail areas of the null hypothesis: that the variances of the numerator and denominator are equal. It can be used for either a one-tailed or two-tailed test. The default is two-tailed, but one-tailed can be computed by setting the optional argument ‘one-tailed-p’ to true.

For a two-tailed test, this function computes the probability that F would be as different from 1.0 (larger or smaller) as it is, if the null hypothesis is true.

For a one-tailed test, this function computes the probability that F would be as LARGE as it is if the first sample’s underlying distribution actually has SMALLER variance that the second’s, where ‘numerator-dof’ and ‘denominator-dof’ is the number of degrees of freedom in the numerator sample and the denominator sample. In other words, this computes the significance level at which the hypothesis “the numerator sample has smaller variance than the denominator sample” can be rejected.

A small numerical value implies a very significant rejection.

The ‘f-statistic’ must be a non-negative floating-point number. The degrees of freedom arguments must be positive integers. The ‘one-tailed-p’ argument is treated as a boolean.

This implementation follows Numerical Recipes in C, section 6.3 and the ‘ftest’ function in section 13.4. Some of the documentation is also drawn from the section 6.3, since I couldn’t improve on their explanation.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: factorial N

Returns the factorial of ‘n,’ which should be a non-negative integer. The result will returned as a floating-point number, single-float if possible, otherwise double-float. If it is returned as a double-float, it won’t necessarily be integral, since the actual computation is

(exp (gamma-ln (1+ n)))

Implementation is loosely based on Numerical Recipes in C, section 6.1. On the TI Explorer, the largest argument that won’t cause a floating overflow is 170.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: factorial-exact N

Returns the factorial of ‘n,’ which should be an integer. The result will returned as an integer or bignum. This implementation is exact, but is more computationally expensive than ‘factorial,’ which is to be preferred.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: factorial-ln N

Returns the natural logarithm of n!; ‘n’ should be an integer. The result will be a single-precision, floating point number. The implementation follows Numerical Recipes in C, section 6.1

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: gamma-incomplete A X

This is an incomplete gamma function, what Numerical Recipes in C calls “gammp.” This function also returns, as the second value, g(a,x). See the manual for more information.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: gamma-ln X

Returns the natural logarithm of the Gamma function evaluated at ‘x.’ Mathematically, the Gamma function is defined to be the integral from 0 to Infinity of t^x exp(-t) dt. The implementation is copied, with extensions for the reflection formula, from Numerical Recipes in C, section 6.1. The argument ‘x’ must be positive. Full accuracy is obtained for x>1. For x<1, the reflection formula is used. The computation is done using double-floats, and the result is a double-float.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: gaussian-cdf X &optional MEAN SD

Computes the cumulative distribution function for a Gaussian random variable (defaults: mean=0.0, s.d.=1.0) evaluated at ‘x.’ The result is the probability of getting a random number less than or equal to ‘x,’ from the given Gaussian distribution.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: gaussian-significance X TAILS &optional MEAN SD

Computes the significance of ‘x’ in a Gaussian distribution with mean=‘mean’ (default 0.0) and standard deviation=‘sd’ (default 1.0); that is, it returns the area which farther from the mean than ‘x’ is.

The null hypothesis is roughly that ‘x’ is zero; you must specify your alternative hypothesis (H1) via the ‘tails’ parameter, which must be :both, :positive or :negative. The first corresponds to a two-tailed test: H1 is that ‘x’ is not zero, but you are not specifying a direction. If the parameter is :positive, H1 is that ‘x’ is positive, and similarly for :negative.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: interquartile-range &rest ARGS

INTERQUARTILE-RANGE (DATA)
The interquartile range is similar to the variance of a sample because both are statistics that measure out “spread out” a sample is. The interquartile range is the difference between the 3/4 quantile (the upper quartile) and the 1/4 quantile (the lower quartile).

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: lagged-correlation SEQUENCE1 SEQUENCE2 LAG

Returns the correlations of ‘sequence1’ with ‘sequence2’ after shifting ‘sequence1’ by ‘lag’. This means that for all n, element n of ‘sequence1’ is paired with element n+‘lag’ of ‘sequence2’, where both of those elements exist.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: linear-regression-brief DV IV

Calculates the main statistics of a linear regression: the slope and intercept of the line, the coefficient of determination, also known as r-square, the standard error of the slope, and the p-value for the regression. This function takes two equal-length sequences of raw data. Note that the dependent variable, as always, comes first in the argument list.

You should first look at your data with a scatter plot to see if a linear model is plausible. See the manual for a fuller explanation of linear regression statistics.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: linear-regression-brief-summaries N X Y X2 Y2 XY

Calculates the main statistics of a linear regression: the slope and intercept of the line, the coefficient of determination, also known as r-square, the standard error of the slope, and the p-value for the regression. This function differs from ‘linear-regression-brief’ in that it takes summary variables: ‘x’ and ‘y’ are the sums of the independent variable and dependent variables, respectively; ‘x2’ and ‘y2’ are the sums of the squares of the independent variable and dependent variables, respectively; and ‘xy’ is the sum of the products of the independent and dependent variables.

You should first look at your data with a scatter plot to see if a linear model is plausible. See the manual for a fuller explanation of linear regression statistics.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: linear-regression-minimal DV IV

Calculates the slope and intercept of the regression line. This function takes two equal-length sequences of raw data. Note that the dependent variable, as always, comes first in the argument list.

You should first look at your data with a scatter plot to see if a linear model is plausible. See the manual for a fuller explanation of linear regression statistics.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: linear-regression-minimal-summaries N X Y X2 Y2 XY

Calculates the slope and intercept of the regression line. This function differs from ‘linear-regression-minimal’ in that it takes summary statistics: ‘x’ and ‘y’ are the sums of the independent variable and dependent variables, respectively; ‘x2’ and ‘y2’ are the sums of the squares of the independent variable and dependent variables, respectively; and ‘xy’ is the sum of the products of the independent and dependent variables.

You should first look at your data with a scatter plot to see if a linear model is plausible. See the manual for a fuller explanation of linear regression statistics.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: linear-regression-verbose DV IV

Calculates almost every statistic of a linear regression: the slope and intercept of the line, the standard error on each, the correlation coefficient, the coefficient of determination, also known as r-square, and an ANOVA table as described in the manual.

This function takes two equal-length sequences of raw data. Note that the dependent variable, as always, comes first in the argument list. If you don’t need all this information, consider using the “-brief,” or “-minimal” functions, which do less computation.

You should first look at your data with a scatter plot to see if a linear model is plausible. See the manual for a fuller explanation of linear regression statistics.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: linear-regression-verbose-summaries N X Y X2 Y2 XY

Calculates almost every statistic of a linear regression: the slope and intercept of the line, the standard error on each, the correlation coefficient, the coefficient of determination, also known as r-square, and an ANOVA table as described in the manual.

If you don’t need all this information, consider using the “-brief” or “-minimal” functions, which do less computation.

This function differs from ‘linear-regression-verbose’ in that it takes summary variables: ‘x’ and ‘y’ are the sums of the independent variable and dependent variables, respectively; ‘x2’ and ‘y2’ are the sums of the squares of the independent variable and dependent variables, respectively; and ‘xy’ is the sum of the products of the independent and dependent variables.

You should first look at your data with a scatter plot to see if a linear model is plausible. See the manual for a fuller explanation of linear regression statistics.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: linear-scale VALUE OLD-MIN OLD-MAX NEW-MIN NEW-MAX

Rescales value linearly from the old-min/old-max scale to the new-min/new-max one.

Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: log2 N

Log of ‘n’ to base 2.

Package

cl-mathstats

Source

binary-math.lisp (file)

Function: matrix-multiply &rest ARGS

Does successive multiplications of each element in ‘args’. If two elements are scalar, then their product is i * j, if a scalar is multiplied by a matrix, then each element in the matrix is multiplied by the scalar, lastly, if two matrices are multiplied then standard matrix multiplication is applied, and the ranks must be such that if ARGi is rank a x b and ARGj is rank c x d, then b must be equal to c.

Package

cl-mathstats

Source

matrix-fns.lisp (file)

Function: matrix-trace MATRIX
Package

cl-mathstats

Source

matrix-fns.lisp (file)

Function: maximum &rest ARGS

MAXIMUM (DATA &KEY START END KEY)
Returns the element of the sequence ‘data’ whose ‘key’ is maximum. Signals ‘no-data’ if there is no data. If there is only one element in the data sequence, that element will be returned, regardless of whether it is valid (a number).

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: mean &rest ARGS

MEAN (DATA &KEY START END KEY)
Returns the arithmetic mean of ‘data,’ which should be a sequence.

Signals ‘no-data’ if there is no data.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: median &rest ARGS

MEDIAN (DATA &KEY START END KEY)
Returns the median of the subsequence of ‘data’ from ‘start’ to ‘end’, using ‘key’. The median is just the 0.5 quantile, and so this function returns the same values as the ‘quantile’ function.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: minimum &rest ARGS

MINIMUM (DATA &KEY START END KEY)
Returns the element of the sequence ‘data’ whose ‘key’ is minimum. Signals ‘no-data’ if there is no data. If there is only one element in the data sequence, that element will be returned, regardless of whether it is valid (a number).

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: mod2 N POWER

Find ‘n’ mod a power of 2.

Package

cl-mathstats

Source

binary-math.lisp (file)

Function: mode &rest ARGS

MODE (DATA &KEY START END KEY)
Returns the most frequent element of ‘data,’ which should be a sequence. The algorithm involves sorting, and so the data must be numbers or the ‘key’ function must produce numbers. Consider ‘sxhash’ if no better function is available. Also returns the number of occurrences of the mode. If there is more than one mode, this returns the first mode, as determined by the sorting of the numbers.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: multiple-linear-regression-arrays DV &rest IVS

This is an internal function for the use of the multiple-linear-regression functions. It takes the lists of values given by CLASP and puts them into a pair of arrays, A and b, suitable for solving the matrix equation Ax=b, to find the regression equation. The values are A and b. The first column of A is the constant 1, so that an intercept will be included in the regression model.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: multiple-linear-regression-brief DV &rest IVS

Let m be the number of independent variables, ‘ivs.’ This function returns a vector of length m which are the coefficients of a linear equation that best predicts the dependent variable, ‘dv,’ in the least squares sense. It also returns, as the second value, the sum of squared deviations of the data from the fitted model, aka SSE, aka chi-square. The third value is the number of degrees of freedom for the chi-square, if you want to test the fit.

This function returns an intermediate amount of information. Consider using the sibling functions -minimal and -verbose if you want less or more information.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: multiple-linear-regression-minimal DV &rest IVS

Let m be the number of independent variables, ‘ivs.’ This function returns a vector of length m which are the coefficients of a linear equation that best predicts the dependent variable, ‘dv,’ in the least squares sense.

This function returns the minimal information for a least squares regression model, namely a list of the coefficients of the ivs, with the constant term first. Consider using the sibling functions -brief and -verbose if you want more information.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: multiple-linear-regression-normal DV &rest IVS

Performs linear regression of the dependent variable, ‘dv,’ on multiple independent variables, ‘ivs.’ Y on multiple X’s, calculating the intercept and regression coefficient. Calculates the F statistic, intercept and the correlation coefficient for Y on X’s.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: multiple-linear-regression-verbose DV &rest IVS

Let m be the number of independent variables, ‘ivs.’ This function returns fourteen values:
1. the intercept
2. a list of coefficients
3. a list of correlations of each iv to the dv and to each iv
4. a list of the t-statistic for each coefficient
5. a list of the standardized coefficients (betas)
6. the fraction of variance accounted for, aka r-square
7. the ratio of MSR (see #12) to MSE (see #13), aka F
8. a list of the portion of the SSR due to each iv
9. a list of the fraction of variance accounted for by each iv
10. the sum of squares of the regression, aka SSR
11. the sum of squares of the residuals, aka SSE, aka chi-square
12. the mean squared error of the regression, aka MSR
13. the mean squared error of the residuals, aka MSE
14. a list of indices of “zeroed” independent variables

This function returns a lot of information about the regression. Consider using the sibling functions -minimal and -brief if you need less information.

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: multiple-modes &rest ARGS

MULTIPLE-MODES (DATA K &KEY START END KEY)
Returns the ‘k’ most frequent elements of ‘data,’ which should be a sequence. The algorithm involves sorting, and so the data must be numbers or the ‘key’ function must produce numbers. Consider #’sxhash if no better function is available. Also returns the number of occurrences of each mode. The value is an association list of modes and their counts. This function is a little more computationally expensive than ‘mode,’ so only use it if you really need multiple modes.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: normalize-matrix M

Returns a new matrix such that the sum of its elements is 1.0

Package

cl-mathstats

Source

matrices.lisp (file)

Function: on-interval X LOWER-BOUND UPPER-BOUND &key LOWER-INCLUSIVE? UPPER-INCLUSIVE?

returns t iff x in the interval

Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: partials-from-parents FROM TO PARENTS-LIST
Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: permutation-count N K

Returns the number of possible ways of taking k elements out of n total.

Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: poisson-cdf K X

Computes the cumulative distribution function for a Poisson random variable with mean ‘x’ evaluated at ‘k.’ The result is the probability that the number of Poisson random events occurring will be between 0 and k-1 inclusive, if the expected number is ‘x.’ The argument ‘k’ should be an integer, while ‘x’ should be a float. The implementation follows Numerical Recipes in C, section 6.2

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: quantile &rest ARGS

QUANTILE (DATA Q &KEY START END KEY)
Returns the element which is the q’th percentile of the data when accessed by ‘key.’ That is, it returns the element such that ‘q’ of the data is smaller than it and 1-‘q’ is above it, where ‘q’ is a number between zero and one, inclusive. For example, if ‘q’ is .5, this returns the median; if ‘q’ is 0, this returns the minimum (although the ‘minimum’ function is more efficient).

This function uses the bisection method, doing linear interpolation between elements i and i+1, where i=floor(q(n-1)). See the manual for more information. The function returns three values: the interpolated quantile and the two elements that determine the interval it was interpolated in. If the quantile was exact, the second two values are the same element of the data.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: r-score NUMBER-LIST-1 NUMBER-LIST-2

Takes two sequences and returns the correlation coefficient. Formula: Sum (Cross-product (Difference-list (number-list-1) Difference-list (number-list-2)) /
(Sqrt (Sum-of-Squares (number-list-1) * Sum-of-Squares (number-list-2)))).

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: radians->degrees RADIANS

Convert radians to degrees. Does not round the result.

Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: range &rest ARGS

RANGE (DATA &KEY START END KEY)
Returns the range of the sequence ‘data.’ Signals ‘no-data’ if there is no data. The range is given by max - min.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: round-to-factor N FACTOR

Equivalent to (* factor (round n factor)). For example, ‘round-to-factor’ of 65 and 60 is 60. Useful for converting to certain units, say when converting minutes to the nearest hours. See also ‘truncate-to-factor.’

Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: safe-exp X

Eliminates floating point underflow for the exponential function. Instead, it just returns 0.0d0

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: scheffe-tests GROUP-MEANS GROUP-SIZES MS-ERROR DF-ERROR

Performs all pairwise comparisons between group means, testing for significance using Scheffe’s F-test. Returns an upper-triangular table in a format described in the manual. Also see the function ‘print-scheffe-table.’

‘Group-means’ and ‘group-sizes’ should be sequences. The arguments ‘ms-error’ and ‘df-error’ are the mean square error within groups and its degrees of freedom, both of which are computed by the analysis of variance. An ANOVA test should always be run first, to see if there are any significant differences.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: significance &rest ARGS

SIGNIFICANCE NIL NIL

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: skewness &rest ARGS

SKEWNESS (DATA &KEY START END KEY)
Returns the skewness of ‘data’, which is the sum of cubed distances from the mean divided by the standard deviation, divided by N.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: smooth-4253h DATA

Smooths ‘data’ by successive smoothing: 4,median; then 2,median; then 5,median; then 3,median; then hanning. The ends are handled by duplicating the end elements. This function is not destructive; it returns a list the same length as ‘data,’ which should be a list of numbers.

Package

cl-mathstats

Source

smoothing.lisp (file)

Function: smooth-hanning DATA

Smooths ‘data’ by replacing each element with the weighted mean of it and its two neighbors. The weights are 1/2 for itself and 1/4 for each neighbor. The ends are handled by duplicating the end elements. This function is not destructive; it returns a list the same length as ‘data,’ which should be a sequence of numbers.

Package

cl-mathstats

Source

smoothing.lisp (file)

Function: smooth-mean-2 DATA

With a window of size two, the median and mean smooth functions are the same.

Package

cl-mathstats

Source

smoothing.lisp (file)

Function: smooth-mean-3 DATA

Smooths ‘data’ by replacing each element with the mean of it and its two neighbors. The ends are handled by duplicating the end elements. This function is not destructive; it returns a list the same length as ‘data,’ which should be a sequence of numbers.

Package

cl-mathstats

Source

smoothing.lisp (file)

Function: smooth-mean-4 DATA

Smooths ‘data’ by replacing each element with the mean of it, its left neighbor, and its two right neighbors. The ends are handled by duplicating the end elements. This function is not destructive; it returns a list the same length as ‘data,’ which should be a sequence of numbers.

Package

cl-mathstats

Source

smoothing.lisp (file)

Function: smooth-mean-5 DATA

Smooths ‘data’ by replacing each element with the median of it, its two left neighbors and its two right neighbors. The ends are handled by duplicating the end elements. This function is not destructive; it returns a list the same length as ‘data,’ which should be a sequence of numbers.

Package

cl-mathstats

Source

smoothing.lisp (file)

Function: smooth-median-2 DATA

Smooths ‘data’ by replacing each element with the median of it and its neighbor on the left. A median of two elements is the same as their mean. The end is handled by duplicating the end element. This function is not destructive; it returns a list the same length as ‘data,’ which should be a sequence of numbers.

Package

cl-mathstats

Source

smoothing.lisp (file)

Function: smooth-median-3 DATA

Smooths ‘data’ by replacing each element with the median of it and its two neighbors. The ends are handled by duplicating the end elements. This function is not destructive; it returns a list the same length as ‘data,’ which should be a sequence of numbers.

Package

cl-mathstats

Source

smoothing.lisp (file)

Function: smooth-median-4 DATA

Smooths ‘data’ by replacing each element with the median of it, its left neighbor, and its two right neighbors. The ends are handled by duplicating the end elements. This function is not destructive; it returns a list the same length as ‘data,’ which should be a sequence of numbers.

Package

cl-mathstats

Source

smoothing.lisp (file)

Function: smooth-median-5 DATA

Smooths ‘data’ by replacing each element with the median of it, its two left neighbors and its two right neighbors. The ends are handled by duplicating the end elements. This function is not destructive; it returns a list the same length as ‘data,’ which should be a sequence of numbers.

Package

cl-mathstats

Source

smoothing.lisp (file)

Function: square X
Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: standard-deviation &rest ARGS

STANDARD-DEVIATION (DATA &KEY START END KEY)
Returns the standard deviation of ‘data,’ which is just the square root of the variance.

Signals ‘no-data’ if there is no data. Signals ‘insufficient-data’ if there is only one datum.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: statistical-summary &rest ARGS

STATISTICAL-SUMMARY (DATA &KEY START END KEY)
Compute the length, minimum, maximum, range, median, mode, mean, variance, standard deviation, and interquartile-range of ‘sequence’ from ‘start’ to ‘end’, accessed by ‘key’.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: students-t-significance T-STATISTIC DOF TAILS

Student’s distribution is much like the Gaussian distribution except with heavier tails, depending on the number of degrees of freedom, ‘dof.’ As ‘dof’ goes to infinity, Student’s distribution approaches the Gaussian. This function computes the significance of ‘t-statistic.’ Values range from 0.0 to 1.0: small values suggest that the null hypothesis—that ‘t-statistic’ is drawn from a t distribution—should be rejected. The ‘t-statistic’ parameter should be a float, while ‘dof’ should be an integer.

The null hypothesis is roughly that ‘t-statistic’ is zero; you must specify your alternative hypothesis (H1) via the ‘tails’ parameter, which must be :both, :positive or :negative. The first corresponds to a two-tailed test: H1 is that ‘t-statistic’ is not zero, but you are not specifying a direction. If the parameter is :positive, H1 is that ‘t-statistic’ is positive, and similarly for :negative.

This implementation follows Numerical Recipes in C, section 6.3.

Package

cl-mathstats

Source

density-fns.lisp (file)

Function: sum-of-array-elements ARRAY
Package

cl-mathstats

Source

matrices.lisp (file)

Function: t-significance &rest ARGS

T-SIGNIFICANCE NIL NIL

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: t-test &rest ARGS

T-TEST (SAMPLE-1 SAMPLE-2 &OPTIONAL (TAILS BOTH) (H0MEAN 0))
Returns the t-statistic for the difference in the means of two samples, which should each be a sequence of numbers. Let D=mean1-mean2. The null hypothesis is that D=0. The alternative hypothesis is specified by ‘tails’: ‘:both’ means D/=0, ‘:positive’ means D>0, and ‘:negative’ means D<0. Unless you’re using :both tails, be careful what order the two samples are in: it matters!

The function also returns the significance, the standard error, and the degrees of freedom. Signals ‘standard-error-is-zero’ if that condition occurs. Signals ‘insufficient-data’ unless there are at least two elements in each sample.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: t-test-matched &rest ARGS

T-TEST-MATCHED (SAMPLE1 SAMPLE2 &OPTIONAL (TAILS BOTH))
Returns the t-statistic for two matched samples, which should be equal-length sequences of numbers. Let D=mean1-mean2. The null hypothesis is that D=0. The alternative hypothesis is specified by ‘tails’: ‘:both’ means D/=0, ‘:positive’ means D>0, and ‘:negative’ means D<0. Unless you’re using :both tails, be careful what order the two samples are in: it matters!

The function also returns the significance, the standard error, and the degrees of freedom. Signals ‘standard-error-is-zero’ if that condition occurs. Signals ‘insufficient-data’ unless there are at least two elements in each sample.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: t-test-one-sample &rest ARGS

T-TEST-ONE-SAMPLE (DATA TAILS &OPTIONAL (H0-MEAN 0) &KEY START END KEY) Returns the t-statistic for the mean of the data, which should be a sequence of numbers. Let D be the sample mean. The null hypothesis is that D equals the ‘H0-mean.’ The alternative hypothesis is specified by ‘tails’: ‘:both’ means D /= H0-mean, ‘:positive’ means D > H0-mean, and ‘:negative’ means D < H0-mean.

The function also returns the significance, the standard error, and the degrees of freedom. Signals ‘zero-variance’ if that condition occurs. Signals ‘insufficient-data’ unless there are at least two elements in the sample.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: times2 I &optional POWER

Multiply ‘i’ by a power of 2.

Package

cl-mathstats

Source

binary-math.lisp (file)

Function: transpose-matrix MATRIX &optional INTO-MATRIX &aux DIM-1 DIM-2
Package

cl-mathstats

Source

matrices.lisp (file)

Function: trimmed-mean &rest ARGS

TRIMMED-MEAN (DATA PERCENTAGE &KEY START END KEY)
Returns a trimmed mean of ‘data.’ A trimmed mean is an ordinary, arithmetic mean of the data, except that an outlying percentage has been discarded. For example, suppose there are ten elements in ‘data,’ and ‘percentage’ is 0.1: the result would be the mean of the middle eight elements, having discarded the biggest and smallest elements. If ‘percentage’ doesn’t result in a whole number of elements being discarded, then a fraction of the remaining biggest and smallest is discarded. For example, suppose ‘data’ is ’(1 2 3 4 5) and ‘percentage’ is 0.25: the result is (.75(2) + 3 + .75(4))/(.75+1+.75) or 3. By convention, the 0.5 trimmed mean is the median, which is always returned as a number.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: trunc2 N POWER

Truncate ‘n’ to a power of 2.

Package

cl-mathstats

Source

binary-math.lisp (file)

Function: truncate-to-factor N FACTOR

Equivalent to (* factor (truncate n factor)). For example, ‘truncate-to-factor’ of 65 and 60 is 60. Useful for converting to certain units, say when converting minutes to hours and minutes. See also ‘round-to-factor.’

Package

cl-mathstats

Source

math-utilities.lisp (file)

Function: tukey-summary &rest ARGS

TUKEY-SUMMARY (DATA &KEY START END KEY)
Computes a Tukey five-number summary of the data. That is, it returns, in increasing order, the extremes and the quartiles: the minimum, the 1/4 quartile, the median, the 3/4 quartile, and the maximum.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: variance &rest ARGS

VARIANCE (DATA &KEY START END KEY)
Returns the variance of ‘data,’ that is, the ‘sum-of-squares’ divided by n-1. Signals ‘no-data’ if there is no data. Signals ‘insufficient-data’ if there is only one datum.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: z-test-one-sample &rest ARGS

Z-TEST-ONE-SAMPLE (DATA TAILS &OPTIONAL (H0-MEAN 0) (H0-STD-DEV 1) &KEY START END KEY)
NIL

Package

cl-mathstats

Source

basic-statistics.lisp (file)


Next: , Previous: , Up: Exported definitions   [Contents][Index]

5.1.4 Generic functions

Generic Function: convert OBJECT TYPE
Package

cl-mathstats

Methods
Method: convert (THING iteratable-container-mixin) (TYPE (eql iteratable-thing))
Source

basic-statistics.lisp (file)

Method: convert (THING sequence) (TYPE (eql iteratable-thing))
Source

basic-statistics.lisp (file)

Method: convert OBJECT TYPE
Source

define-statistical-fun.lisp (file)

Generic Function: cross-product NUMBER-LIST-1 NUMBER-LIST-2
Package

cl-mathstats

Methods
Method: cross-product (NUMBER-LIST-1 sequence) (NUMBER-LIST-2 sequence)

Takes two sequences of numbers and returns a sequence of cross products. Formula XYi = Xi * Yi.

Source

basic-statistics.lisp (file)

Generic Function: dot-product SEQUENCE-1 SEQUENCE-2

http://en.wikipedia.org/wiki/Dot_product

Package

cl-mathstats

Source

api.lisp (file)

Methods
Method: dot-product (NUMBER-LIST-1 sequence) (NUMBER-LIST-2 sequence)

Takes two sequences of numbers and returns the dot product.

Source

basic-statistics.lisp (file)


Previous: , Up: Exported definitions   [Contents][Index]

5.1.5 Classes

Class: anova-one-way-variables ()
Package

cl-mathstats

Source

anova.lisp (file)

Direct superclasses

composite-statistic (class)

Direct slots
Slot: anova-table
Slot: means-list
Slot: scheffe-table
Slot: sst-alt
Class: anova-two-way-variables ()
Package

cl-mathstats

Source

anova.lisp (file)

Direct superclasses

composite-statistic (class)

Direct slots
Slot: anova-table
Class: anova-two-way-variables-unequal-cell-sizes ()
Package

cl-mathstats

Source

anova.lisp (file)

Direct superclasses

composite-statistic (class)

Direct slots
Slot: anova-table
Slot: ab-matrix
Slot: row-totals
Slot: column-totals
Slot: grand-totla
Slot: a-labels
Slot: b-labels
Class: autocorrelation ()
Package

cl-mathstats

Source

correlation-regression.lisp (file)

Direct superclasses

simple-statistic (class)

Class: confidence-interval ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

composite-statistic (class)

Direct subclasses
Direct slots
Slot: value
Slot: lower-bound
Slot: upper-bound
Class: confidence-interval-proportion ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses
Class: confidence-interval-t ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses
Class: confidence-interval-z ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses
Class: correlation ()
Package

cl-mathstats

Source

correlation-regression.lisp (file)

Direct superclasses

simple-statistic (class)

Class: covariance ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Class: cross-correlation ()
Package

cl-mathstats

Source

correlation-regression.lisp (file)

Direct superclasses

simple-statistic (class)

Class: d-test ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses
Direct slots
Slot: count
Slot: times
Class: data-length ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: interquartile-range ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: maximum ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: mean ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: median ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: minimum ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: mode ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: multiple-modes ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Class: quantile ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Class: range ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: significance ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

composite-statistic (class)

Direct subclasses
Direct slots
Slot: statistic
Slot: level
Class: skewness ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: standard-deviation ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: statistical-summary ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses
Class: t-significance ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses
Direct subclasses
Direct slots
Slot: std-error
Slot: dof
Class: t-test ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses
Class: t-test-matched ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses
Class: t-test-one-sample ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses
Class: trimmed-mean ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Class: tukey-summary ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

composite-statistic (class)

Direct slots
Slot: minimum
Slot: first-quartile
Slot: median
Slot: third-quartile
Slot: maximum
Class: variance ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

simple-statistic (class)

Direct subclasses

statistical-summary (class)

Class: z-test-one-sample ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Direct superclasses

Previous: , Up: Definitions   [Contents][Index]

5.2 Internal definitions


Next: , Previous: , Up: Internal definitions   [Contents][Index]

5.2.1 Constants

Constant: +log-pi+
Package

cl-mathstats

Source

density-fns.lisp (file)

Constant: +sqrt-pi+
Package

cl-mathstats

Source

density-fns.lisp (file)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

5.2.2 Special variables

Special Variable: *continous-data-window-divisor*
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Special Variable: *continuous-variable-uniqueness-factor*
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Special Variable: *create-statistical-objects*
Package

cl-mathstats

Source

define-statistical-fun.lisp (file)

Special Variable: *gaussian-cdf-signals-zero-standard-deviation-error*
Package

cl-mathstats

Source

parameters.lisp (file)

Special Variable: *temporary-table*

A temporary table. This avoids consing.

Package

cl-mathstats

Source

utilities.lisp (file)

Special Variable: *temporary-vector*

A temporary vector for use by statistical functions such as ‘quantile,’ which uses it for sorting data. This avoids consing or rearranging the user’s data.

Package

cl-mathstats

Source

utilities.lisp (file)

Special Variable: *way-too-big-contingency-table-dimension*
Package

cl-mathstats

Source

basic-statistics.lisp (file)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

5.2.3 Macros

Macro: aref1 A I
Package

cl-mathstats

Source

svd.lisp (file)

Macro: aref11 A I J
Package

cl-mathstats

Source

svd.lisp (file)

Macro: check-type-of-arg ARG-NAME PREDICATE TYPE-STRING &optional ERROR-TYPE-NAME

Generate error if the value of ARG-NAME doesn’t satisfy PREDICATE.
PREDICATE is a function name (a symbol) or an expression to compute. TYPE-STRING is a string to use in the error message, such as "a list". ERROR-TYPE-NAME is a keyword that tells condition handlers what type was desired.

Package

cl-mathstats

Source

matrices.lisp (file)

Macro: define-statistic NAME &optional SUPERCLASSES SLOTS VALUES ARGUMENT-TYPES LAMBDA-LIST &body BODY

In clasp, statistical objects have two parts, a class which stores the various parts of the object and a computing function which computes the value of the object from arguments. The define-statistic macro allows the definition of new statistical types. The define-statistic macro must be provided with all the information necessary to create a statistical object, that is, everything required to create a new class, everything required to create a computing function and some information to connect the two. This last part consists of a list of arguments and their types and a list which determines how the values of a statistical function should be used to fill the slots of a statistical object.

When define-statistic is invoked, two things happen, first a class is defined which is a subclass of ’statistic and any other named ‘superclasses’. Second, a pair of functions is defined. ‘clasp-statistics::name’ is an internal function which has the supplied ‘body’ and ‘lambda-list’ and must return as many values as there are slots in the class ‘name’. The function ‘name’ is also defined, it is basically a wrapper function which converts its arguments to those which are accepted by ‘body’ and then calls ‘clasp-statistics::name’. The parameter clasp:*create-statistical-objects* determines whether the wrapper function packages the values returned by the intern function into a statistical object or just returns them as multiple values.

The ‘argument-types’ argument must be an alist in which the keys are the names of arguments as given in ‘lambda-list’ and the values are lisp types which those arguments will be converted to before calling the internal statistical function. The primary purpose of this is to allow for coersion of clasp variables to sequences, but any coercion which is allowed by lisp is acceptable. The ‘values’ argument is intended to allow the programmer to specify which slots in the statistical object are filled by which of the values returned by the statistical function. By default, the order of the values is assumed to be direct slots in order of specification, inherited slots in order of specification in the superclasses which are also statistics.

Package

cl-mathstats

Source

define-statistical-fun.lisp (file)

Macro: sign-df A B
Package

cl-mathstats

Source

svd.lisp (file)

Macro: sign-sf A B
Package

cl-mathstats

Source

svd.lisp (file)

Macro: start/end CALL-FORM START-N END-N
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Macro: with-routine-error-handling &body BODY
Package

cl-mathstats

Source

define-statistical-fun.lisp (file)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

5.2.4 Functions

Function: 1-or-2d-arrayp ARRAY
Package

cl-mathstats

Source

matrices.lisp (file)

Function: anova-one-way-groups DATA &optional SCHEFFE-TESTS-P CONFIDENCE-INTERVALS

Performs a one-way analysis of variance (ANOVA) on the ‘data,’ which should
be a sequence of sequences, where each interior sequence is the data for a particular group. Furthermore, each sequence should consist entirely of numbers, and each should have at least 2 elements.

The significance of the result indicates that the group means are not all equal; that is, at least two of the groups have significantly different means. If there were only two groups, this would be semantically equivalent to an unmatched, two-tailed t-test, so you can think of the one-way ANOVA as a multi-group, two-tailed t-test.

This function returns five values: 1. an ANOVA table; 2. a list a group means; 3. either a Scheffe table or nil depending on ‘scheffe-tests-p’; 4. an alternate value for SST; and 5. a list of confidence intervals in the form ‘(,mean ,lower ,upper) for each group, if ‘confidence-intervals’ is a number between zero and one, giving the kind of confidence interval, such as 0.9. The fourth value is only interesting if you think there are numerical accuracy problems; it should be approximately equal to the SST value in the ANOVA table. This function differs from ‘anova-one-way-variables’ only in its input representation. See the manual for more information.

Package

cl-mathstats

Source

anova.lisp (file)

Function: anova-one-way-variables-internal IV DV &optional SCHEFFE-TESTS-P CONFIDENCE-INTERVALS

See ANOVA-ONE-WAY-VARIABLES

Package

cl-mathstats

Source

anova.lisp (file)

Function: anova-two-way-groups DATA-ARRAY

Calculates the analysis of variance when there are two factors that may affect the dependent variable. Because the input is represented as an array, we can refer to these two factors as the row-effect and the column effect. Unlike the one-way ANOVA, there are mathematical difficulties with the two-way ANOVA if there are unequal cell sizes; therefore, we require all cells to be the same size, and so the input is a three-dimensional array.

The result of the analysis is an anova-table, as described in the manual. This function differs from ‘anova-two-way-variables’ only in its input representation. See the manual for further discussion of analysis of variance.

Package

cl-mathstats

Source

anova.lisp (file)

Function: anova-two-way-variables-internal DV IV1 IV2

See ANOVA-TWO-WAY-VARIABLES

Package

cl-mathstats

Source

anova.lisp (file)

Function: anova-two-way-variables-unequal-cell-sizes-internal IV1 IV2 DV

See ANOVA-TWO-WAY-VARIABLES-UNEQUAL-CELL-SIZES

Package

cl-mathstats

Source

anova.lisp (file)

Function: autocorrelation-internal SAMPLE MAX-LAG &optional MIN-LAG

See AUTOCORRELATION

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: chi-square-2x2 V1 V2

Performs a chi-square test for independence of the two variables, ‘v1’ and ‘v2.’ These should be categorial variables with only two values; the function will construct a 2x2 contingency table by counting the number of occurrences of each combination of the variables. See the manual for more details.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: chi-square-2x2-counts A B C D &optional YATES

Runs a chi-square test for association on a simple 2 x 2 table. If ‘yates’ is nil, the correction for continuity is not done; default is t.

Returns the chi-square statistic and the significance of the value.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: chi-square-rxc V1 V2

Performs a chi-square test for independence of the two variables, ‘v1’ and ‘v2.’ These should be categorial variables; the function will construct a contingency table by counting the number of occurrences of each combination of the variables. See the manual for more details.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: chi-square-rxc-counts CONTINGENCY-TABLE

Calculates the chi-square statistic and corresponding p-value for the given contingency table. The result says whether the row factor is independent of the column factor. Does not apply Yate’s correction.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: confidence-interval-internal ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: confidence-interval-proportion-internal X N CONFIDENCE

See CONFIDENCE-INTERVAL-PROPORTION

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: confidence-interval-t-internal DATA CONFIDENCE

See CONFIDENCE-INTERVAL-T

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: confidence-interval-z-internal DATA CONFIDENCE

See CONFIDENCE-INTERVAL-Z

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: confidence-interval-z-summaries MEAN STANDARD-ERROR CONFIDENCE

This function is just like ‘confidence-interval-z,’ except that instead of its arguments being the actual data, it takes the following summary statistics: ‘mean’, a point estimator of the mean of some normally distributed population; and the ‘standard-error’ of the estimator, that is, the estimated standard deviation of the normal population. ‘Confidence’ should be a number between 0 and 1, exclusive.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: correlation-internal SAMPLE1 SAMPLE2 &rest ARGS &key START1 END1 START2 END2

See CORRELATION

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: covariance-internal SAMPLE1 SAMPLE2 &rest ARGS &key START1 END1 START2 END2

See COVARIANCE

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: cross-correlation-internal SEQUENCE1 SEQUENCE2 MAX-LAG &optional MIN-LAG

See CROSS-CORRELATION

Package

cl-mathstats

Source

correlation-regression.lisp (file)

Function: d-test-internal SAMPLE-1 SAMPLE-2 TAILS &key TIMES H0MEAN

See D-TEST

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: data-continuous-p SEQUENCE
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: data-length-internal DATA &key START END KEY

See DATA-LENGTH

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: difference-list NUMBER-LIST

Takes a sequence of numbers and returns a sequence of differences from the mean.
Formula: xi = Xi - Mean (X).

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: error-function-complement-short-1 Y Z
Package

cl-mathstats

Source

density-fns.lisp (file)

Function: error-function-complement-short-2 Y
Package

cl-mathstats

Source

density-fns.lisp (file)

Function: fill-2d-array ARRAY LIST
Package

cl-mathstats

Source

matrices.lisp (file)

Function: find-critical-value P-FUNCTION P-VALUE &optional X-TOLERANCE Y-TOLERANCE

Returns the critical value of some statistic. The function ‘p-function’ should be a unary function mapping statistics—x values—to their significance—p values. The function will find the value of x such that the p-value is ‘p-value.’ The function works by binary search. A secant method might be better, but this seems to be acceptably fast. Only positive values of x are considered, and ‘p-function’ should be monotonically decreasing from its value at x=0. The binary search ends when either the function value is within ‘y-tolerance’ of ‘p-value’ or the size of the search region shrinks to less than ‘x-tolerance.’

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: g-test CONTINGENCY-TABLE &optional EXPECTED-VALUE-MATRIX ERROR-P

Calculates the G-test for a contingency table. The formula for the
G-test statistic is

2 * sum[f_ij log [f_ij/f-hat_ij]]

where f_ij is the ith by jth cell in the table and f-hat_ij is the
expected value of that cell. If an expected-value-matrix is supplied,
it must be the same size as table and it is used for expected values,
in which case the G-test is a test of goodness-of-fit. If the
expected value matrix is unsupplied, it is calculated from using the
formula

e_ij = [f_i* * f_*j] / f_**

where f_i*, f_*j and f_** are the row, column and grand totals
respectively. In this case, the G-test is a test of independence. The degrees of freedom is the same as for the chi-square statistic and the significance is obtained by comparing

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: inner-product SAMPLE1 SAMPLE2 &key START1 END1 START2 END2

Returns the inner product of the two samples, which should be sequences of numbers. The inner product, also called the dot product or vector product, is the sum of the pairwise multiplication of the numbers. Stops when either sample runs out; it doesn’t check that they have the same length.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: interquartile-range-internal DATA &rest STANDARD-ARGS

See INTERQUARTILE-RANGE

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: invert-matrix MATRIX &optional INTO-MATRIX

If matrix is singular returns nil, else returns its inverse. If into-matrix is supplied, inverse is returned in it, otherwise a new array is created.

Package

cl-mathstats

Source

matrices.lisp (file)

Function: invert-matrix-iterate MATRIX &optional INTO-MATRIX

If matrix is singular returns nil, else returns the inverse of matrix. Uses iterative improvement until no further improvement is possible.

Package

cl-mathstats

Source

matrices.lisp (file)

Function: list-2d-array ARRAY
Package

cl-mathstats

Source

matrices.lisp (file)

Function: make-3d-table DV IV1 IV2

Collects the ‘dv’ values for each unique combination of an element of ‘v1’ and an element of ‘v2.’ Returns a three-dimensional table of dv values.

Package

cl-mathstats

Source

anova.lisp (file)

Function: make-contingency-table V1 V2

Counts each unique combination of an element of ‘v1’ and an element of ‘v2.’ Returns a two-dimensional table of integers.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: matrix-addition &rest ARGS
Package

cl-mathstats

Source

matrix-fns.lisp (file)

Function: matrix-norm MATRIX

Returns the norm of matrix.
The norm is the maximum over the rows of the sum of the abs of the columns.

Package

cl-mathstats

Source

matrices.lisp (file)

Function: matrix-plus-matrix MAT1 MAT2

Adds two matrices together

Package

cl-mathstats

Source

matrix-fns.lisp (file)

Function: matrix-plus-scalar MATRIX SCALAR

Add a scalar value to a matrix

Package

cl-mathstats

Source

matrix-fns.lisp (file)

Function: matrix-times-matrix MAT1 MAT2

Multiplies two matrices together

Package

cl-mathstats

Source

matrix-fns.lisp (file)

Function: matrix-times-scalar MATRIX SCALAR

Multiply a matrix by a scalar value

Package

cl-mathstats

Source

matrix-fns.lisp (file)

Function: matrix-times-scalar! MATRIX SCALAR

Multiply a matrix by a scalar value

Package

cl-mathstats

Source

matrix-fns.lisp (file)

Function: maximum-internal DATA &rest STANDARD-ARGS &key START END KEY

See MAXIMUM

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: mean-internal DATA &rest STANDARD-ARGS &key START END KEY

See MEAN

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: median-internal DATA &rest STANDARD-ARGS &key START END KEY

See MEDIAN

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: minimum-internal DATA &rest STANDARD-ARGS &key START END KEY

See MINIMUM

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: mode-for-continuous-data DATA &rest STANDARD-ARGS &key START END KEY WINDOW

Returns the most frequent element of ‘data,’ which should be a sequence. The algorithm involves sorting, and so the data must be numbers or the ‘key’ function must produce numbers. Consider ‘sxhash’ if no better function is available. Also returns the number of occurrences of the mode. If there is more than one mode, this returns the first mode, as determined by the sorting of the numbers.

Keep in mind that if the data has multiple runs of like values that are bigger than the window size (currently defaults to 10% of the size of the data) this function will blindly pick the first one. If this is the case you probabaly should be calling ‘mode’ instead of this function.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: mode-internal DATA &rest STANDARD-ARGS &key START END KEY

See MODE

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: multiple-modes-internal DATA K &rest STANDARD-ARGS &key START END KEY

See MULTIPLE-MODES

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: multiply-matrices MATRIX-1 MATRIX-2 &optional MATRIX-3 &aux SAVED-MATRIX-3

Multiply matrices MATRIX-1 and MATRIX-2, storing into MATRIX-3 if supplied.
If MATRIX-3 is not supplied, then a new (ART-Q type) array is returned, else
MATRIX-3 must have exactly the right dimensions for holding the result of the multiplication. Both MATRIX-1 and MATRIX-2 must be either one- or two-diimensional.
The first dimension of MATRIX-2 must equal the second dimension of MATRIX-1, unless MATRIX-1 is one-dimensional, when the first dimensions must match (thus allowing multiplications of the form VECTOR x MATRIX)

Package

cl-mathstats

Source

matrices.lisp (file)

Function: print-anova-table ANOVA-TABLE &optional STREAM

Prints ‘anova-table’ on ‘stream.’

Package

cl-mathstats

Source

anova.lisp (file)

Function: print-scheffe-table SCHEFFE-TABLE &optional GROUP-MEANS STREAM

Prints ‘scheffe-table’ on ‘stream.’ If the original one-way anova data had N groups, the Scheffe table prints as an n-1 x n-1 upper-triangular table. If ‘group-means’ is given, it should be a list of the group means, which will be printed along with the table.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: pythag-df A B

Computes square root of a*a + b*b without destructive overflow or underflow.

Package

cl-mathstats

Source

svd.lisp (file)

Function: pythag-sf A B

Computes square root of a*a + b*b without destructive overflow or underflow.

Package

cl-mathstats

Source

svd.lisp (file)

Function: quantile-internal DATA Q &rest STANDARD-ARGS &key START END KEY

See QUANTILE

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: range-internal DATA &rest STANDARD-ARGS &key START END KEY

See RANGE

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: reduce-matrix MAT

Uses the Gauss-Jordan reduction method to reduce a matrix.

Package

cl-mathstats

Source

matrix-fns.lisp (file)

Function: remove-&rest LIST

Removes the ’&rest arg’ part from a lambda-list (strictly for documentation purposes.

Package

cl-mathstats

Source

define-statistical-fun.lisp (file)

Function: scalar-matrix-multiply SCALAR MATRIX

Multiplies a matrix by a scalar value in the form M[i,j] = s*M[i,j].

Package

cl-mathstats

Source

matrices.lisp (file)

Function: significance-internal ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: singular-value-decomposition MATRIX

Returns as three values the U W and V of singular value decomposition. If you have already consed up these matrices, you should call ‘svdcmp-sf’ or ‘svdcmp-df’ directly. The input matrix is preserved.

Package

cl-mathstats

Source

svd.lisp (file)

Function: skewness-internal DATA &rest STANDARD-ARGS &key START END KEY

See SKEWNESS

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: smart-mode SEQUENCE &rest ARGS
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: standard-deviation-internal DATA &rest STANDARD-ARGS &key START END KEY

See STANDARD-DEVIATION

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: statistical-summary-internal DATA &rest STANDARD-ARGS &key START END KEY

See STATISTICAL-SUMMARY

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: sum-list NUMBER-LIST

Takes a sequence of numbers and returns their sum. Formula: Sum(X).

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: sum-of-squares DATA &rest STANDARD-ARGS &key START END KEY

Returns the sum of squared distances from the mean of ‘data’.

Signals ‘no-data’ if there is no data.

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: svbksb-df U W V M N B X &optional TMP

Solves A X = B for a vector ‘X,’ where A is specified by the mxn array U, ‘n’ vector W, and nxn matrix V as returned by svdcmp. ‘m’ and ‘n’ are the dimensions of ‘A,’ and will be equal for square matrices. ‘B’ is the 1xm input vector for the right-hand side. ‘X’ is the 1xn output solution vector. All arrays are of double-floats. No input quantities are destroyed, so the routine may be called sequentially with different B’s. See the discussion in Numerical Recipes in C, section 2.6.

This routine assumes that near zero singular values have already been zeroed. It returns no values, storing the result in ‘X.’ It does use some auxiliary storage, which can be passed in as ‘tmp,’ a double-float array of length ‘n,’ if you want to avoid consing.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svbksb-sf U W V M N B X &optional TMP

Solves A X = B for a vector ‘X,’ where A is specified by the mxn array U, ‘n’ vector W, and nxn matrix V as returned by svdcmp. ‘m’ and ‘n’ are the dimensions of ‘A,’ and will be equal for square matrices. ‘B’ is the 1xm input vector for the right-hand side. ‘X’ is the 1xn output solution vector. All arrays are of single-floats. No input quantities are destroyed, so the routine may be called sequentially with different B’s. See the discussion in Numerical Recipes in C, section 2.6.

This routine assumes that near zero singular values have already been zeroed. It returns no values, storing the result in ‘X.’ It does use some auxiliary storage, which can be passed in as ‘tmp,’ a single-float array of length ‘n,’ if you want to avoid consing.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svd-back-substitute U W V B

Returns the solution vector to the Ax=b, where A has been decomposed into ‘u,’ ‘w’ and ‘v’ by ‘singular-value-decomposition.’ This function is just a minor wrapping of ‘svbksb-sf’ and ‘svbksb-df.’

Package

cl-mathstats

Source

svd.lisp (file)

Function: svd-inverse-fast-df U W V &optional A-1 TMP

Computes the inverse of a matrix that has been decomposed into ‘u,’ ‘w’ and ‘v’ by singular value decomposition. It assumes the “small” elements of ‘w’ have already been zeroed. It computes the inverse by taking advantage of the known zeros in the full 2-dimensional ‘w’ matrix. It uses the backsubstitution algorithm, only with the B vectors fixed at the columns of the identity matrix, which lets us take advantage of its zeros. It’s about twice as fast as the slow version and conses a lot less. Note that if you are computing the inverse merely to solve one or more systems of equations, you are better off using the decomposition and backsubstitution routines directly.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svd-inverse-fast-sf U W V &optional A-1 TMP

Computes the inverse of a matrix that has been decomposed into ‘u,’ ‘w’ and ‘v’ by singular value decomposition. It assumes the “small” elements of ‘w’ have already been zeroed. It computes the inverse by taking advantage of the known zeros in the full 2-dimensional ‘w’ matrix. It uses the backsubstitution algorithm, only with the B vectors fixed at the columns of the identity matrix, which lets us take advantage of its zeros. It’s about twice as fast as the slow version and conses a lot less. Note that if you are computing the inverse merely to solve one or more systems of equations, you are better off using the decomposition and backsubstitution routines directly.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svd-inverse-slow-df U W V &optional A-1

Computes the inverse of a matrix that has been decomposed into ‘u,’ ‘w’ and ‘v’ by singular value decomposition. It assumes the “small” elements of ‘w’ have already been zeroed. It computes the inverse by constructing a diagonal matrix ‘w2’ from ‘w’ (which is just a vector of the diagonal elements, and then explicitly multiplying u^t w2 and v. Note that if you are computing the inverse merely to solve one or more systems of equations, you are better off using the decomposition and backsubstitution routines directly.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svd-inverse-slow-sf U W V &optional A-1

Computes the inverse of a matrix that has been decomposed into ‘u,’ ‘w’ and ‘v’ by singular value decomposition. It assumes the “small” elements of ‘w’ have already been zeroed. It computes the inverse by constructing a diagonal matrix ‘w2’ from ‘w’ (which is just a vector of the diagonal elements, and then explicitly multiplying u^t w2 and v. Note that if you are computing the inverse merely to solve one or more systems of equations, you are better off using the decomposition and backsubstitution routines directly.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svd-matrix-inverse A &optional SINGULARITY-THRESHOLD

Use singular value decomposition to compute the inverse of ‘A.’ If an exact inverse is not possible, then zero the otherwise infinite inverted singular value and compute the inverse. The inverse is returned; ‘A’ is not destroyed. If you’re using this to solve several systems of equations, you’re better off computing the singular value decomposition and using it several times, because this function computes it anew each time.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svd-solve-linear-system MATRIX B-VECTOR &optional REPORT? THRESHOLD

Returns solution of linear system matrix * solution = b-vector. Employs the singular value decomposition method. See the discussion in Numerical Recipes in C, section 2.6, especially as to the semantics of ‘threshold.’

Package

cl-mathstats

Source

svd.lisp (file)

Function: svd-zero W &optional THRESHOLD REPORT?

If the relative magnitude of an element in ‘w’ compared to the largest element is less than ‘threshold,’ then zero that element. Returns a list of indices of the zeroed elements. This function is just a convenient wrapper for ‘svzero-sf’ and ‘svzero-df.’

Package

cl-mathstats

Source

svd.lisp (file)

Function: svdcmp-df A M N W V &optional RV1

Given an ‘m’x‘n’ matrix ‘A,’ this routine computes its singular value decomposition, A = U W V^T. The matrix U replaces ‘A’ on output. The diagonal matrix of singular values W is output as a vector ‘W’ of length ‘n.’ The matrix ‘V’ – not the transpose V^T – is output as an ‘n’x‘n’ matrix ‘V.’ The row dimension ‘m’ must be greater or equal to ‘n’; if it is smaller, then ‘A’ should be filled up to square with zero rows. See the discussion in Numerical Recipes in C, section 2.6.

This routine returns no values, storing the results in ‘A,’ ‘W,’ and ‘V.’ It does use some auxiliary storage, which can be passed in as ‘rv1,’ a double-float array of length ‘n,’ if you want to avoid consing.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svdcmp-sf A M N W V &optional RV1

Given an ‘m’x‘n’ matrix ‘A,’ this routine computes its singular value decomposition, A = U W V^T. The matrix U replaces ‘A’ on output. The diagonal matrix of singular values W is output as a vector ‘W’ of length ‘n.’ The matrix ‘V’ – not the transpose V^T – is output as an ‘n’x‘n’ matrix ‘V.’ The row dimension ‘m’ must be greater or equal to ‘n’; if it is smaller, then ‘A’ should be filled up to square with zero rows. See the discussion in Numerical Recipes in C, section 2.6.

This routine returns no values, storing the results in ‘A,’ ‘W,’ and ‘V.’ It does use some auxiliary storage, which can be passed in as ‘rv1,’ a single-float array of length ‘n,’ if you want to avoid consing. All input arrays should be of single-floats.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svdvar V W &optional CVM

Given ‘v’ and ‘w’ as computed by singular value decomposition, computes the covariance matrix among the predictors. Based on Numerical Recipes in C, section 15.4, algorithm ‘svdvar.’ The covariance matrix is returned. It can be supplied as the third argument.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svzero-df W N THRESHOLD &optional REPORT?

If the relative magnitude of an element in ‘w’ compared to the largest element is less than ‘threshold,’ then zero that element. If ‘report?’ is true, the indices of zeroed elements are printed. Returns a list of the indices of zeroed elements. This routine uses double-floats.

Package

cl-mathstats

Source

svd.lisp (file)

Function: svzero-sf W N THRESHOLD &optional REPORT?

If the relative magnitude of an element in ‘w’ compared to the largest element is less than ‘threshold,’ then zero that element. If ‘report?’ is true, the indices of zeroed elements are printed. Returns a list of indices of the zeroed elements. This routine uses single-floats.

Package

cl-mathstats

Source

svd.lisp (file)

Function: t-significance-internal ()
Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: t-test-internal SAMPLE-1 SAMPLE-2 &optional TAILS H0MEAN

See T-TEST

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: t-test-matched-internal SAMPLE1 SAMPLE2 &optional TAILS

See T-TEST-MATCHED

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: t-test-one-sample-internal DATA TAILS &optional H0-MEAN &rest STANDARD-ARGS &key START END KEY

See T-TEST-ONE-SAMPLE

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: trimmed-mean-internal DATA PERCENTAGE &rest STANDARD-ARGS &key START END KEY

See TRIMMED-MEAN

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: tukey-summary-internal DATA &rest STANDARD-ARGS &key START END KEY

See TUKEY-SUMMARY

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: variance-internal DATA &rest STANDARD-ARGS &key START END KEY

See VARIANCE

Package

cl-mathstats

Source

basic-statistics.lisp (file)

Function: z-test-one-sample-internal DATA TAILS &optional H0-MEAN H0-STD-DEV &rest STANDARD-ARGS &key START END KEY

See Z-TEST-ONE-SAMPLE

Package

cl-mathstats

Source

basic-statistics.lisp (file)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

5.2.5 Generic functions

Generic Function: composite-statistic-p IT
Package

cl-mathstats

Methods
Method: composite-statistic-p (IT composite-statistic)
Source

define-statistical-fun.lisp (file)

Method: composite-statistic-p IT
Source

define-statistical-fun.lisp (file)

Generic Function: make-statistic TYPE &rest ARGS
Package

cl-mathstats

Methods
Method: make-statistic TYPE &rest ARGS
Source

define-statistical-fun.lisp (file)

Generic Function: simple-statistic-p IT
Package

cl-mathstats

Methods
Method: simple-statistic-p (IT simple-statistic)
Source

define-statistical-fun.lisp (file)

Method: simple-statistic-p IT
Source

define-statistical-fun.lisp (file)

Generic Function: statisticp IT
Package

cl-mathstats

Methods
Method: statisticp (IT statistic)
Source

define-statistical-fun.lisp (file)

Method: statisticp IT
Source

define-statistical-fun.lisp (file)


Next: , Previous: , Up: Internal definitions   [Contents][Index]

5.2.6 Conditions

Condition: data-error ()
Package

cl-mathstats

Source

class-defs.lisp (file)

Direct superclasses

error (condition)

Direct subclasses
Condition: enormous-contingency-table ()
Package

cl-mathstats

Source

class-defs.lisp (file)

Direct superclasses

condition (condition)

Condition: insufficient-data ()
Package

cl-mathstats

Source

class-defs.lisp (file)

Direct superclasses

data-error (condition)

Direct subclasses

no-data (condition)

Condition: no-data ()
Package

cl-mathstats

Source

class-defs.lisp (file)

Direct superclasses

insufficient-data (condition)

Condition: not-binary-variables ()
Package

cl-mathstats

Source

class-defs.lisp (file)

Direct superclasses

data-error (condition)

Condition: unmatched-sequences ()
Package

cl-mathstats

Source

class-defs.lisp (file)

Direct superclasses

data-error (condition)

Condition: zero-standard-deviation ()
Package

cl-mathstats

Source

class-defs.lisp (file)

Direct superclasses

data-error (condition)

Condition: zero-variance ()
Package

cl-mathstats

Source

class-defs.lisp (file)

Direct superclasses

data-error (condition)


Previous: , Up: Internal definitions   [Contents][Index]

5.2.7 Classes

Class: composite-statistic ()
Package

cl-mathstats

Source

define-statistical-fun.lisp (file)

Direct superclasses

statistic (class)

Direct subclasses
Direct methods

composite-statistic-p (method)

Class: data ()
Package

cl-mathstats

Source

define-statistical-fun.lisp (file)

Direct superclasses

standard-object (class)

Direct subclasses

statistic (class)

Class: simple-statistic ()
Package

cl-mathstats

Source

define-statistical-fun.lisp (file)

Direct superclasses

statistic (class)

Direct subclasses
Direct methods

simple-statistic-p (method)

Class: statistic ()
Package

cl-mathstats

Source

define-statistical-fun.lisp (file)

Direct superclasses

data (class)

Direct subclasses
Direct methods

statisticp (method)


Previous: , Up: Top   [Contents][Index]

Appendix A Indexes


Next: , Previous: , Up: Indexes   [Contents][Index]

A.1 Concepts

Jump to:   C   F   L   M   O  
Index Entry  Section

C
cl-mathstats.asd: The cl-mathstats<dot>asd file
cl-mathstats/dev: The cl-mathstats/dev module
cl-mathstats/dev/anova.lisp: The cl-mathstats/dev/anova<dot>lisp file
cl-mathstats/dev/api.lisp: The cl-mathstats/dev/api<dot>lisp file
cl-mathstats/dev/basic-statistics.lisp: The cl-mathstats/dev/basic-statistics<dot>lisp file
cl-mathstats/dev/binary-math.lisp: The cl-mathstats/dev/binary-math<dot>lisp file
cl-mathstats/dev/class-defs.lisp: The cl-mathstats/dev/class-defs<dot>lisp file
cl-mathstats/dev/correlation-regression.lisp: The cl-mathstats/dev/correlation-regression<dot>lisp file
cl-mathstats/dev/define-statistical-fun.lisp: The cl-mathstats/dev/define-statistical-fun<dot>lisp file
cl-mathstats/dev/definitions.lisp: The cl-mathstats/dev/definitions<dot>lisp file
cl-mathstats/dev/density-fns.lisp: The cl-mathstats/dev/density-fns<dot>lisp file
cl-mathstats/dev/math-utilities.lisp: The cl-mathstats/dev/math-utilities<dot>lisp file
cl-mathstats/dev/matrices.lisp: The cl-mathstats/dev/matrices<dot>lisp file
cl-mathstats/dev/matrix-fns.lisp: The cl-mathstats/dev/matrix-fns<dot>lisp file
cl-mathstats/dev/package.lisp: The cl-mathstats/dev/package<dot>lisp file
cl-mathstats/dev/parameters.lisp: The cl-mathstats/dev/parameters<dot>lisp file
cl-mathstats/dev/smoothing.lisp: The cl-mathstats/dev/smoothing<dot>lisp file
cl-mathstats/dev/svd.lisp: The cl-mathstats/dev/svd<dot>lisp file
cl-mathstats/dev/utilities.lisp: The cl-mathstats/dev/utilities<dot>lisp file
cl-mathstats/website: The cl-mathstats/website module
cl-mathstats/website/source: The cl-mathstats/website/source module
cl-mathstats/website/source/index.md: The cl-mathstats/website/source/index<dot>md file

F
File, Lisp, cl-mathstats.asd: The cl-mathstats<dot>asd file
File, Lisp, cl-mathstats/dev/anova.lisp: The cl-mathstats/dev/anova<dot>lisp file
File, Lisp, cl-mathstats/dev/api.lisp: The cl-mathstats/dev/api<dot>lisp file
File, Lisp, cl-mathstats/dev/basic-statistics.lisp: The cl-mathstats/dev/basic-statistics<dot>lisp file
File, Lisp, cl-mathstats/dev/binary-math.lisp: The cl-mathstats/dev/binary-math<dot>lisp file
File, Lisp, cl-mathstats/dev/class-defs.lisp: The cl-mathstats/dev/class-defs<dot>lisp file
File, Lisp, cl-mathstats/dev/correlation-regression.lisp: The cl-mathstats/dev/correlation-regression<dot>lisp file
File, Lisp, cl-mathstats/dev/define-statistical-fun.lisp: The cl-mathstats/dev/define-statistical-fun<dot>lisp file
File, Lisp, cl-mathstats/dev/definitions.lisp: The cl-mathstats/dev/definitions<dot>lisp file
File, Lisp, cl-mathstats/dev/density-fns.lisp: The cl-mathstats/dev/density-fns<dot>lisp file
File, Lisp, cl-mathstats/dev/math-utilities.lisp: The cl-mathstats/dev/math-utilities<dot>lisp file
File, Lisp, cl-mathstats/dev/matrices.lisp: The cl-mathstats/dev/matrices<dot>lisp file
File, Lisp, cl-mathstats/dev/matrix-fns.lisp: The cl-mathstats/dev/matrix-fns<dot>lisp file
File, Lisp, cl-mathstats/dev/package.lisp: The cl-mathstats/dev/package<dot>lisp file
File, Lisp, cl-mathstats/dev/parameters.lisp: The cl-mathstats/dev/parameters<dot>lisp file
File, Lisp, cl-mathstats/dev/smoothing.lisp: The cl-mathstats/dev/smoothing<dot>lisp file
File, Lisp, cl-mathstats/dev/svd.lisp: The cl-mathstats/dev/svd<dot>lisp file
File, Lisp, cl-mathstats/dev/utilities.lisp: The cl-mathstats/dev/utilities<dot>lisp file
File, other, cl-mathstats/website/source/index.md: The cl-mathstats/website/source/index<dot>md file

L
Lisp File, cl-mathstats.asd: The cl-mathstats<dot>asd file
Lisp File, cl-mathstats/dev/anova.lisp: The cl-mathstats/dev/anova<dot>lisp file
Lisp File, cl-mathstats/dev/api.lisp: The cl-mathstats/dev/api<dot>lisp file
Lisp File, cl-mathstats/dev/basic-statistics.lisp: The cl-mathstats/dev/basic-statistics<dot>lisp file
Lisp File, cl-mathstats/dev/binary-math.lisp: The cl-mathstats/dev/binary-math<dot>lisp file
Lisp File, cl-mathstats/dev/class-defs.lisp: The cl-mathstats/dev/class-defs<dot>lisp file
Lisp File, cl-mathstats/dev/correlation-regression.lisp: The cl-mathstats/dev/correlation-regression<dot>lisp file
Lisp File, cl-mathstats/dev/define-statistical-fun.lisp: The cl-mathstats/dev/define-statistical-fun<dot>lisp file
Lisp File, cl-mathstats/dev/definitions.lisp: The cl-mathstats/dev/definitions<dot>lisp file
Lisp File, cl-mathstats/dev/density-fns.lisp: The cl-mathstats/dev/density-fns<dot>lisp file
Lisp File, cl-mathstats/dev/math-utilities.lisp: The cl-mathstats/dev/math-utilities<dot>lisp file
Lisp File, cl-mathstats/dev/matrices.lisp: The cl-mathstats/dev/matrices<dot>lisp file
Lisp File, cl-mathstats/dev/matrix-fns.lisp: The cl-mathstats/dev/matrix-fns<dot>lisp file
Lisp File, cl-mathstats/dev/package.lisp: The cl-mathstats/dev/package<dot>lisp file
Lisp File, cl-mathstats/dev/parameters.lisp: The cl-mathstats/dev/parameters<dot>lisp file
Lisp File, cl-mathstats/dev/smoothing.lisp: The cl-mathstats/dev/smoothing<dot>lisp file
Lisp File, cl-mathstats/dev/svd.lisp: The cl-mathstats/dev/svd<dot>lisp file
Lisp File, cl-mathstats/dev/utilities.lisp: The cl-mathstats/dev/utilities<dot>lisp file

M
Module, cl-mathstats/dev: The cl-mathstats/dev module
Module, cl-mathstats/website: The cl-mathstats/website module
Module, cl-mathstats/website/source: The cl-mathstats/website/source module

O
Other File, cl-mathstats/website/source/index.md: The cl-mathstats/website/source/index<dot>md file

Jump to:   C   F   L   M   O  

Next: , Previous: , Up: Indexes   [Contents][Index]

A.2 Functions

Jump to:   1  
A   B   C   D   E   F   G   I   L   M   N   O   P   Q   R   S   T   U   V   W   Z  
Index Entry  Section

1
1-or-2d-arrayp: Internal functions

A
anova-one-way-groups: Internal functions
anova-one-way-variables: Exported functions
anova-one-way-variables-internal: Internal functions
anova-two-way-groups: Internal functions
anova-two-way-variables: Exported functions
anova-two-way-variables-internal: Internal functions
anova-two-way-variables-unequal-cell-sizes: Exported functions
anova-two-way-variables-unequal-cell-sizes-internal: Internal functions
aref1: Internal macros
aref11: Internal macros
autocorrelation: Exported functions
autocorrelation-internal: Internal functions

B
beta: Exported functions
beta-incomplete: Exported functions
binomial-cdf: Exported functions
binomial-cdf-exact: Exported functions
binomial-coefficient: Exported functions
binomial-coefficient-exact: Exported functions
binomial-probability: Exported functions
binomial-probability-exact: Exported functions

C
check-type-of-arg: Internal macros
chi-square-2x2: Internal functions
chi-square-2x2-counts: Internal functions
chi-square-rxc: Internal functions
chi-square-rxc-counts: Internal functions
chi-square-significance: Exported functions
combination-count: Exported functions
composite-statistic-p: Internal generic functions
composite-statistic-p: Internal generic functions
composite-statistic-p: Internal generic functions
confidence-interval: Exported functions
confidence-interval-internal: Internal functions
confidence-interval-proportion: Exported functions
confidence-interval-proportion-internal: Internal functions
confidence-interval-t: Exported functions
confidence-interval-t-internal: Internal functions
confidence-interval-t-summaries: Exported functions
confidence-interval-z: Exported functions
confidence-interval-z-internal: Internal functions
confidence-interval-z-summaries: Internal functions
convert: Exported generic functions
convert: Exported generic functions
convert: Exported generic functions
convert: Exported generic functions
correlation: Exported functions
correlation-from-summaries: Exported functions
correlation-internal: Internal functions
correlation-matrix: Exported functions
covariance: Exported functions
covariance-internal: Internal functions
cross-correlation: Exported functions
cross-correlation-internal: Internal functions
cross-product: Exported generic functions
cross-product: Exported generic functions

D
d-test: Exported functions
d-test-internal: Internal functions
data-continuous-p: Internal functions
data-length: Exported functions
data-length-internal: Internal functions
define-statistic: Internal macros
degrees->radians: Exported functions
difference-list: Internal functions
div2: Exported functions
dot-product: Exported generic functions
dot-product: Exported generic functions

E
ensure-float: Exported functions
error-function: Exported functions
error-function-complement: Exported functions
error-function-complement-short-1: Internal functions
error-function-complement-short-2: Internal functions
exp2: Exported functions
extract-unique-values: Exported functions

F
f-measure: Exported functions
f-significance: Exported functions
factorial: Exported functions
factorial-exact: Exported functions
factorial-ln: Exported functions
fill-2d-array: Internal functions
find-critical-value: Internal functions
Function, 1-or-2d-arrayp: Internal functions
Function, anova-one-way-groups: Internal functions
Function, anova-one-way-variables: Exported functions
Function, anova-one-way-variables-internal: Internal functions
Function, anova-two-way-groups: Internal functions
Function, anova-two-way-variables: Exported functions
Function, anova-two-way-variables-internal: Internal functions
Function, anova-two-way-variables-unequal-cell-sizes: Exported functions
Function, anova-two-way-variables-unequal-cell-sizes-internal: Internal functions
Function, autocorrelation: Exported functions
Function, autocorrelation-internal: Internal functions
Function, beta: Exported functions
Function, beta-incomplete: Exported functions
Function, binomial-cdf: Exported functions
Function, binomial-cdf-exact: Exported functions
Function, binomial-coefficient: Exported functions
Function, binomial-coefficient-exact: Exported functions
Function, binomial-probability: Exported functions
Function, binomial-probability-exact: Exported functions
Function, chi-square-2x2: Internal functions
Function, chi-square-2x2-counts: Internal functions
Function, chi-square-rxc: Internal functions
Function, chi-square-rxc-counts: Internal functions
Function, chi-square-significance: Exported functions
Function, combination-count: Exported functions
Function, confidence-interval: Exported functions
Function, confidence-interval-internal: Internal functions
Function, confidence-interval-proportion: Exported functions
Function, confidence-interval-proportion-internal: Internal functions
Function, confidence-interval-t: Exported functions
Function, confidence-interval-t-internal: Internal functions
Function, confidence-interval-t-summaries: Exported functions
Function, confidence-interval-z: Exported functions
Function, confidence-interval-z-internal: Internal functions
Function, confidence-interval-z-summaries: Internal functions
Function, correlation: Exported functions
Function, correlation-from-summaries: Exported functions
Function, correlation-internal: Internal functions
Function, correlation-matrix: Exported functions
Function, covariance: Exported functions
Function, covariance-internal: Internal functions
Function, cross-correlation: Exported functions
Function, cross-correlation-internal: Internal functions
Function, d-test: Exported functions
Function, d-test-internal: Internal functions
Function, data-continuous-p: Internal functions
Function, data-length: Exported functions
Function, data-length-internal: Internal functions
Function, degrees->radians: Exported functions
Function, difference-list: Internal functions
Function, div2: Exported functions
Function, ensure-float: Exported functions
Function, error-function: Exported functions
Function, error-function-complement: Exported functions
Function, error-function-complement-short-1: Internal functions
Function, error-function-complement-short-2: Internal functions
Function, exp2: Exported functions
Function, extract-unique-values: Exported functions
Function, f-measure: Exported functions
Function, f-significance: Exported functions
Function, factorial: Exported functions
Function, factorial-exact: Exported functions
Function, factorial-ln: Exported functions
Function, fill-2d-array: Internal functions
Function, find-critical-value: Internal functions
Function, g-test: Internal functions
Function, gamma-incomplete: Exported functions
Function, gamma-ln: Exported functions
Function, gaussian-cdf: Exported functions
Function, gaussian-significance: Exported functions
Function, inner-product: Internal functions
Function, interquartile-range: Exported functions
Function, interquartile-range-internal: Internal functions
Function, invert-matrix: Internal functions
Function, invert-matrix-iterate: Internal functions
Function, lagged-correlation: Exported functions
Function, linear-regression-brief: Exported functions
Function, linear-regression-brief-summaries: Exported functions
Function, linear-regression-minimal: Exported functions
Function, linear-regression-minimal-summaries: Exported functions
Function, linear-regression-verbose: Exported functions
Function, linear-regression-verbose-summaries: Exported functions
Function, linear-scale: Exported functions
Function, list-2d-array: Internal functions
Function, log2: Exported functions
Function, make-3d-table: Internal functions
Function, make-contingency-table: Internal functions
Function, matrix-addition: Internal functions
Function, matrix-multiply: Exported functions
Function, matrix-norm: Internal functions
Function, matrix-plus-matrix: Internal functions
Function, matrix-plus-scalar: Internal functions
Function, matrix-times-matrix: Internal functions
Function, matrix-times-scalar: Internal functions
Function, matrix-times-scalar!: Internal functions
Function, matrix-trace: Exported functions
Function, maximum: Exported functions
Function, maximum-internal: Internal functions
Function, mean: Exported functions
Function, mean-internal: Internal functions
Function, median: Exported functions
Function, median-internal: Internal functions
Function, minimum: Exported functions
Function, minimum-internal: Internal functions
Function, mod2: Exported functions
Function, mode: Exported functions
Function, mode-for-continuous-data: Internal functions
Function, mode-internal: Internal functions
Function, multiple-linear-regression-arrays: Exported functions
Function, multiple-linear-regression-brief: Exported functions
Function, multiple-linear-regression-minimal: Exported functions
Function, multiple-linear-regression-normal: Exported functions
Function, multiple-linear-regression-verbose: Exported functions
Function, multiple-modes: Exported functions
Function, multiple-modes-internal: Internal functions
Function, multiply-matrices: Internal functions
Function, normalize-matrix: Exported functions
Function, on-interval: Exported functions
Function, partials-from-parents: Exported functions
Function, permutation-count: Exported functions
Function, poisson-cdf: Exported functions
Function, print-anova-table: Internal functions
Function, print-scheffe-table: Internal functions
Function, pythag-df: Internal functions
Function, pythag-sf: Internal functions
Function, quantile: Exported functions
Function, quantile-internal: Internal functions
Function, r-score: Exported functions
Function, radians->degrees: Exported functions
Function, range: Exported functions
Function, range-internal: Internal functions
Function, reduce-matrix: Internal functions
Function, remove-&rest: Internal functions
Function, round-to-factor: Exported functions
Function, safe-exp: Exported functions
Function, scalar-matrix-multiply: Internal functions
Function, scheffe-tests: Exported functions
Function, significance: Exported functions
Function, significance-internal: Internal functions
Function, singular-value-decomposition: Internal functions
Function, skewness: Exported functions
Function, skewness-internal: Internal functions
Function, smart-mode: Internal functions
Function, smooth-4253h: Exported functions
Function, smooth-hanning: Exported functions
Function, smooth-mean-2: Exported functions
Function, smooth-mean-3: Exported functions
Function, smooth-mean-4: Exported functions
Function, smooth-mean-5: Exported functions
Function, smooth-median-2: Exported functions
Function, smooth-median-3: Exported functions
Function, smooth-median-4: Exported functions
Function, smooth-median-5: Exported functions
Function, square: Exported functions
Function, standard-deviation: Exported functions
Function, standard-deviation-internal: Internal functions
Function, statistical-summary: Exported functions
Function, statistical-summary-internal: Internal functions
Function, students-t-significance: Exported functions
Function, sum-list: Internal functions
Function, sum-of-array-elements: Exported functions
Function, sum-of-squares: Internal functions
Function, svbksb-df: Internal functions
Function, svbksb-sf: Internal functions
Function, svd-back-substitute: Internal functions
Function, svd-inverse-fast-df: Internal functions
Function, svd-inverse-fast-sf: Internal functions
Function, svd-inverse-slow-df: Internal functions
Function, svd-inverse-slow-sf: Internal functions
Function, svd-matrix-inverse: Internal functions
Function, svd-solve-linear-system: Internal functions
Function, svd-zero: Internal functions
Function, svdcmp-df: Internal functions
Function, svdcmp-sf: Internal functions
Function, svdvar: Internal functions
Function, svzero-df: Internal functions
Function, svzero-sf: Internal functions
Function, t-significance: Exported functions
Function, t-significance-internal: Internal functions
Function, t-test: Exported functions
Function, t-test-internal: Internal functions
Function, t-test-matched: Exported functions
Function, t-test-matched-internal: Internal functions
Function, t-test-one-sample: Exported functions
Function, t-test-one-sample-internal: Internal functions
Function, times2: Exported functions
Function, transpose-matrix: Exported functions
Function, trimmed-mean: Exported functions
Function, trimmed-mean-internal: Internal functions
Function, trunc2: Exported functions
Function, truncate-to-factor: Exported functions
Function, tukey-summary: Exported functions
Function, tukey-summary-internal: Internal functions
Function, variance: Exported functions
Function, variance-internal: Internal functions
Function, z-test-one-sample: Exported functions
Function, z-test-one-sample-internal: Internal functions

G
g-test: Internal functions
gamma-incomplete: Exported functions
gamma-ln: Exported functions
gaussian-cdf: Exported functions
gaussian-significance: Exported functions
Generic Function, composite-statistic-p: Internal generic functions
Generic Function, convert: Exported generic functions
Generic Function, cross-product: Exported generic functions
Generic Function, dot-product: Exported generic functions
Generic Function, make-statistic: Internal generic functions
Generic Function, simple-statistic-p: Internal generic functions
Generic Function, statisticp: Internal generic functions

I
inner-product: Internal functions
interquartile-range: Exported functions
interquartile-range-internal: Internal functions
invert-matrix: Internal functions
invert-matrix-iterate: Internal functions

L
lagged-correlation: Exported functions
linear-regression-brief: Exported functions
linear-regression-brief-summaries: Exported functions
linear-regression-minimal: Exported functions
linear-regression-minimal-summaries: Exported functions
linear-regression-verbose: Exported functions
linear-regression-verbose-summaries: Exported functions
linear-scale: Exported functions
list-2d-array: Internal functions
log2: Exported functions

M
Macro, aref1: Internal macros
Macro, aref11: Internal macros
Macro, check-type-of-arg: Internal macros
Macro, define-statistic: Internal macros
Macro, sign-df: Internal macros
Macro, sign-sf: Internal macros
Macro, start/end: Internal macros
Macro, underflow-goes-to-zero: Exported macros
Macro, with-routine-error-handling: Internal macros
Macro, with-temp-table: Exported macros
Macro, with-temp-vector: Exported macros
make-3d-table: Internal functions
make-contingency-table: Internal functions
make-statistic: Internal generic functions
make-statistic: Internal generic functions
matrix-addition: Internal functions
matrix-multiply: Exported functions
matrix-norm: Internal functions
matrix-plus-matrix: Internal functions
matrix-plus-scalar: Internal functions
matrix-times-matrix: Internal functions
matrix-times-scalar: Internal functions
matrix-times-scalar!: Internal functions
matrix-trace: Exported functions
maximum: Exported functions
maximum-internal: Internal functions
mean: Exported functions
mean-internal: Internal functions
median: Exported functions
median-internal: Internal functions
Method, composite-statistic-p: Internal generic functions
Method, composite-statistic-p: Internal generic functions
Method, convert: Exported generic functions
Method, convert: Exported generic functions
Method, convert: Exported generic functions
Method, cross-product: Exported generic functions
Method, dot-product: Exported generic functions
Method, make-statistic: Internal generic functions
Method, simple-statistic-p: Internal generic functions
Method, simple-statistic-p: Internal generic functions
Method, statisticp: Internal generic functions
Method, statisticp: Internal generic functions
minimum: Exported functions
minimum-internal: Internal functions
mod2: Exported functions
mode: Exported functions
mode-for-continuous-data: Internal functions
mode-internal: Internal functions
multiple-linear-regression-arrays: Exported functions
multiple-linear-regression-brief: Exported functions
multiple-linear-regression-minimal: Exported functions
multiple-linear-regression-normal: Exported functions
multiple-linear-regression-verbose: Exported functions
multiple-modes: Exported functions
multiple-modes-internal: Internal functions
multiply-matrices: Internal functions

N
normalize-matrix: Exported functions

O
on-interval: Exported functions

P
partials-from-parents: Exported functions
permutation-count: Exported functions
poisson-cdf: Exported functions
print-anova-table: Internal functions
print-scheffe-table: Internal functions
pythag-df: Internal functions
pythag-sf: Internal functions

Q
quantile: Exported functions
quantile-internal: Internal functions

R
r-score: Exported functions
radians->degrees: Exported functions
range: Exported functions
range-internal: Internal functions
reduce-matrix: Internal functions
remove-&rest: Internal functions
round-to-factor: Exported functions

S
safe-exp: Exported functions
scalar-matrix-multiply: Internal functions
scheffe-tests: Exported functions
sign-df: Internal macros
sign-sf: Internal macros
significance: Exported functions
significance-internal: Internal functions
simple-statistic-p: Internal generic functions
simple-statistic-p: Internal generic functions
simple-statistic-p: Internal generic functions
singular-value-decomposition: Internal functions
skewness: Exported functions
skewness-internal: Internal functions
smart-mode: Internal functions
smooth-4253h: Exported functions
smooth-hanning: Exported functions
smooth-mean-2: Exported functions
smooth-mean-3: Exported functions
smooth-mean-4: Exported functions
smooth-mean-5: Exported functions
smooth-median-2: Exported functions
smooth-median-3: Exported functions
smooth-median-4: Exported functions
smooth-median-5: Exported functions
square: Exported functions
standard-deviation: Exported functions
standard-deviation-internal: Internal functions
start/end: Internal macros
statistical-summary: Exported functions
statistical-summary-internal: Internal functions
statisticp: Internal generic functions
statisticp: Internal generic functions
statisticp: Internal generic functions
students-t-significance: Exported functions
sum-list: Internal functions
sum-of-array-elements: Exported functions
sum-of-squares: Internal functions
svbksb-df: Internal functions
svbksb-sf: Internal functions
svd-back-substitute: Internal functions
svd-inverse-fast-df: Internal functions
svd-inverse-fast-sf: Internal functions
svd-inverse-slow-df: Internal functions
svd-inverse-slow-sf: Internal functions
svd-matrix-inverse: Internal functions
svd-solve-linear-system: Internal functions
svd-zero: Internal functions
svdcmp-df: Internal functions
svdcmp-sf: Internal functions
svdvar: Internal functions
svzero-df: Internal functions
svzero-sf: Internal functions

T
t-significance: Exported functions
t-significance-internal: Internal functions
t-test: Exported functions
t-test-internal: Internal functions
t-test-matched: Exported functions
t-test-matched-internal: Internal functions
t-test-one-sample: Exported functions
t-test-one-sample-internal: Internal functions
times2: Exported functions
transpose-matrix: Exported functions
trimmed-mean: Exported functions
trimmed-mean-internal: Internal functions
trunc2: Exported functions
truncate-to-factor: Exported functions
tukey-summary: Exported functions
tukey-summary-internal: Internal functions

U
underflow-goes-to-zero: Exported macros

V
variance: Exported functions
variance-internal: Internal functions

W
with-routine-error-handling: Internal macros
with-temp-table: Exported macros
with-temp-vector: Exported macros

Z
z-test-one-sample: Exported functions
z-test-one-sample-internal: Internal functions

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Next: , Previous: , Up: Indexes   [Contents][Index]

A.3 Variables

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Index Entry  Section

*
*continous-data-window-divisor*: Internal special variables
*continuous-variable-uniqueness-factor*: Internal special variables
*create-statistical-objects*: Internal special variables
*gaussian-cdf-signals-zero-standard-deviation-error*: Internal special variables
*temporary-table*: Internal special variables
*temporary-vector*: Internal special variables
*way-too-big-contingency-table-dimension*: Internal special variables

+
+0degrees+: Exported constants
+10degrees+: Exported constants
+120degrees+: Exported constants
+135degrees+: Exported constants
+150degrees+: Exported constants
+15degrees+: Exported constants
+180degrees+: Exported constants
+210degrees+: Exported constants
+225degrees+: Exported constants
+240degrees+: Exported constants
+270degrees+: Exported constants
+300degrees+: Exported constants
+30degrees+: Exported constants
+315degrees+: Exported constants
+330degrees+: Exported constants
+360degrees+: Exported constants
+45degrees+: Exported constants
+5degrees+: Exported constants
+60degrees+: Exported constants
+90degrees+: Exported constants
+e+: Exported constants
+log-pi+: Internal constants
+sqrt-pi+: Internal constants

2
2fpi: Exported constants

A
a-labels: Exported classes
ab-matrix: Exported classes
anova-table: Exported classes
anova-table: Exported classes
anova-table: Exported classes

B
b-labels: Exported classes

C
column-totals: Exported classes
Constant, +0degrees+: Exported constants
Constant, +10degrees+: Exported constants
Constant, +120degrees+: Exported constants
Constant, +135degrees+: Exported constants
Constant, +150degrees+: Exported constants
Constant, +15degrees+: Exported constants
Constant, +180degrees+: Exported constants
Constant, +210degrees+: Exported constants
Constant, +225degrees+: Exported constants
Constant, +240degrees+: Exported constants
Constant, +270degrees+: Exported constants
Constant, +300degrees+: Exported constants
Constant, +30degrees+: Exported constants
Constant, +315degrees+: Exported constants
Constant, +330degrees+: Exported constants
Constant, +360degrees+: Exported constants
Constant, +45degrees+: Exported constants
Constant, +5degrees+: Exported constants
Constant, +60degrees+: Exported constants
Constant, +90degrees+: Exported constants
Constant, +e+: Exported constants
Constant, +log-pi+: Internal constants
Constant, +sqrt-pi+: Internal constants
Constant, 2fpi: Exported constants
Constant, fpi: Exported constants
count: Exported classes

D
dof: Exported classes

F
first-quartile: Exported classes
fpi: Exported constants

G
grand-totla: Exported classes

L
level: Exported classes
lower-bound: Exported classes

M
maximum: Exported classes
means-list: Exported classes
median: Exported classes
minimum: Exported classes

R
row-totals: Exported classes

S
scheffe-table: Exported classes
Slot, a-labels: Exported classes
Slot, ab-matrix: Exported classes
Slot, anova-table: Exported classes
Slot, anova-table: Exported classes
Slot, anova-table: Exported classes
Slot, b-labels: Exported classes
Slot, column-totals: Exported classes
Slot, count: Exported classes
Slot, dof: Exported classes
Slot, first-quartile: Exported classes
Slot, grand-totla: Exported classes
Slot, level: Exported classes
Slot, lower-bound: Exported classes
Slot, maximum: Exported classes
Slot, means-list: Exported classes
Slot, median: Exported classes
Slot, minimum: Exported classes
Slot, row-totals: Exported classes
Slot, scheffe-table: Exported classes
Slot, sst-alt: Exported classes
Slot, statistic: Exported classes
Slot, std-error: Exported classes
Slot, third-quartile: Exported classes
Slot, times: Exported classes
Slot, upper-bound: Exported classes
Slot, value: Exported classes
Special Variable, *continous-data-window-divisor*: Internal special variables
Special Variable, *continuous-variable-uniqueness-factor*: Internal special variables
Special Variable, *create-statistical-objects*: Internal special variables
Special Variable, *gaussian-cdf-signals-zero-standard-deviation-error*: Internal special variables
Special Variable, *temporary-table*: Internal special variables
Special Variable, *temporary-vector*: Internal special variables
Special Variable, *way-too-big-contingency-table-dimension*: Internal special variables
sst-alt: Exported classes
statistic: Exported classes
std-error: Exported classes

T
third-quartile: Exported classes
times: Exported classes

U
upper-bound: Exported classes

V
value: Exported classes

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Previous: , Up: Indexes   [Contents][Index]

A.4 Data types

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Index Entry  Section

A
anova-one-way-variables: Exported classes
anova-two-way-variables: Exported classes
anova-two-way-variables-unequal-cell-sizes: Exported classes
asdf-cl-mathstats: The asdf-cl-mathstats package
autocorrelation: Exported classes

C
cl-mathstats: The cl-mathstats system
cl-mathstats: The cl-mathstats package
Class, anova-one-way-variables: Exported classes
Class, anova-two-way-variables: Exported classes
Class, anova-two-way-variables-unequal-cell-sizes: Exported classes
Class, autocorrelation: Exported classes
Class, composite-statistic: Internal classes
Class, confidence-interval: Exported classes
Class, confidence-interval-proportion: Exported classes
Class, confidence-interval-t: Exported classes
Class, confidence-interval-z: Exported classes
Class, correlation: Exported classes
Class, covariance: Exported classes
Class, cross-correlation: Exported classes
Class, d-test: Exported classes
Class, data: Internal classes
Class, data-length: Exported classes
Class, interquartile-range: Exported classes
Class, maximum: Exported classes
Class, mean: Exported classes
Class, median: Exported classes
Class, minimum: Exported classes
Class, mode: Exported classes
Class, multiple-modes: Exported classes
Class, quantile: Exported classes
Class, range: Exported classes
Class, significance: Exported classes
Class, simple-statistic: Internal classes
Class, skewness: Exported classes
Class, standard-deviation: Exported classes
Class, statistic: Internal classes
Class, statistical-summary: Exported classes
Class, t-significance: Exported classes
Class, t-test: Exported classes
Class, t-test-matched: Exported classes
Class, t-test-one-sample: Exported classes
Class, trimmed-mean: Exported classes
Class, tukey-summary: Exported classes
Class, variance: Exported classes
Class, z-test-one-sample: Exported classes
composite-statistic: Internal classes
Condition, data-error: Internal conditions
Condition, enormous-contingency-table: Internal conditions
Condition, insufficient-data: Internal conditions
Condition, no-data: Internal conditions
Condition, not-binary-variables: Internal conditions
Condition, unmatched-sequences: Internal conditions
Condition, zero-standard-deviation: Internal conditions
Condition, zero-variance: Internal conditions
confidence-interval: Exported classes
confidence-interval-proportion: Exported classes
confidence-interval-t: Exported classes
confidence-interval-z: Exported classes
correlation: Exported classes
covariance: Exported classes
cross-correlation: Exported classes

D
d-test: Exported classes
data: Internal classes
data-error: Internal conditions
data-length: Exported classes

E
enormous-contingency-table: Internal conditions

I
insufficient-data: Internal conditions
interquartile-range: Exported classes

M
maximum: Exported classes
mean: Exported classes
median: Exported classes
minimum: Exported classes
mode: Exported classes
multiple-modes: Exported classes

N
no-data: Internal conditions
not-binary-variables: Internal conditions

P
Package, asdf-cl-mathstats: The asdf-cl-mathstats package
Package, cl-mathstats: The cl-mathstats package

Q
quantile: Exported classes

R
range: Exported classes

S
significance: Exported classes
simple-statistic: Internal classes
skewness: Exported classes
standard-deviation: Exported classes
statistic: Internal classes
statistical-summary: Exported classes
System, cl-mathstats: The cl-mathstats system

T
t-significance: Exported classes
t-test: Exported classes
t-test-matched: Exported classes
t-test-one-sample: Exported classes
trimmed-mean: Exported classes
tukey-summary: Exported classes

U
unmatched-sequences: Internal conditions

V
variance: Exported classes

Z
z-test-one-sample: Exported classes
zero-standard-deviation: Internal conditions
zero-variance: Internal conditions

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