GNU Octave Manual Version 3 by John W. Eaton, David Bateman, Søren Hauberg Paperback (6"x9"), 568 pages ISBN 095461206X RRP £24.95 ($39.95) 
24.6 Distributions
Octave has functions for computing the Probability Density Function (PDF), the Cumulative Distribution function (CDF), and the quantile (the inverse of the CDF) of a large number of distributions.
The following table summarizes the supported distributions (in alphabetical order).
Distribution  CDF  Quantile
 
Beta Distribution  betapdf
 betacdf
 betainv

Binomial Distribution  binopdf
 binocdf
 binoinv

Cauchy Distribution  cauchy_pdf
 cauchy_cdf
 cauchy_inv

ChiSquare Distribution  chi2pdf
 chi2cdf
 chi2inv

Univariate Discrete Distribution  discrete_pdf
 discrete_cdf
 discrete_inv

Empirical Distribution  empirical_pdf
 empirical_cdf
 empirical_inv

Exponential Distribution  exppdf
 expcdf
 expinv

F Distribution  fpdf
 fcdf
 finv

Gamma Distribution  gampdf
 gamcdf
 gaminv

Geometric Distribution  geopdf
 geocdf
 geoinv

Hypergeometric Distribution  hygepdf
 hygecdf
 hygeinv

Kolmogorov Smirnov Distribution  Not Available  kolmogorov_smirnov_cdf
 Not Available

Laplace Distribution  laplace_pdf
 laplace_cdf
 laplace_inv

Logistic Distribution  logistic_pdf
 logistic_cdf
 logistic_inv

LogNormal Distribution  lognpdf
 logncdf
 logninv

Pascal Distribution  nbinpdf
 nbincdf
 nbininv

Univariate Normal Distribution  normpdf
 normcdf
 norminv

Poisson Distribution  poisspdf
 poisscdf
 poissinv

t (Student) Distribution  tpdf
 tcdf
 tinv

Univariate Discrete Distribution  unidpdf
 unidcdf
 unidinv

Uniform Distribution  unifpdf
 unifcdf
 unifinv

Weibull Distribution  wblpdf
 wblcdf
 wblinv

 Function File: betacdf (x, a, b)
 For each element of x, returns the CDF at x of the beta distribution with parameters a and b, i.e., PROB (beta (a, b) <= x).
 Function File: betainv (x, a, b)
 For each component of x, compute the quantile (the inverse of the CDF) at x of the Beta distribution with parameters a and b.
 Function File: betapdf (x, a, b)
 For each element of x, returns the PDF at x of the beta distribution with parameters a and b.
 Function File: binocdf (x, n, p)
 For each element of x, compute the CDF at x of the binomial distribution with parameters n and p.
 Function File: binoinv (x, n, p)
 For each element of x, compute the quantile at x of the binomial distribution with parameters n and p.
 Function File: binopdf (x, n, p)
 For each element of x, compute the probability density function (PDF) at x of the binomial distribution with parameters n and p.
 Function File: cauchy_cdf (x, lambda, sigma)
 For each element of x, compute the cumulative distribution function (CDF) at x of the Cauchy distribution with location parameter lambda and scale parameter sigma. Default values are lambda = 0, sigma = 1.
 Function File: cauchy_inv (x, lambda, sigma)
 For each element of x, compute the quantile (the inverse of the CDF) at x of the Cauchy distribution with location parameter lambda and scale parameter sigma. Default values are lambda = 0, sigma = 1.
 Function File: cauchy_pdf (x, lambda, sigma)
 For each element of x, compute the probability density function (PDF) at x of the Cauchy distribution with location parameter lambda and scale parameter sigma > 0. Default values are lambda = 0, sigma = 1.
 Function File: chi2cdf (x, n)
 For each element of x, compute the cumulative distribution function (CDF) at x of the chisquare distribution with n degrees of freedom.
 Function File: chi2inv (x, n)
 For each element of x, compute the quantile (the inverse of the CDF) at x of the chisquare distribution with n degrees of freedom.
 Function File: chisquare_pdf (x, n)
 For each element of x, compute the probability density function (PDF) at x of the chisquare distribution with n degrees of freedom.
 Function File: discrete_cdf (x, v, p)
 For each element of x, compute the cumulative distribution function (CDF) at x of a univariate discrete distribution which assumes the values in v with probabilities p.
 Function File: discrete_inv (x, v, p)
 For each component of x, compute the quantile (the inverse of the CDF) at x of the univariate distribution which assumes the values in v with probabilities p.
 Function File: discrete_pdf (x, v, p)
 For each element of x, compute the probability density function (PDF) at x of a univariate discrete distribution which assumes the values in v with probabilities p.
 Function File: empirical_cdf (x, data)
 For each element of x, compute the cumulative distribution function (CDF) at x of the empirical distribution obtained from the univariate sample data.
 Function File: empirical_inv (x, data)
 For each element of x, compute the quantile (the inverse of the CDF) at x of the empirical distribution obtained from the univariate sample data.
 Function File: empirical_pdf (x, data)
 For each element of x, compute the probability density function (PDF) at x of the empirical distribution obtained from the univariate sample data.
 Function File: expcdf (x, lambda)
 For each element of x, compute the cumulative distribution function (CDF) at x of the exponential distribution with mean lambda. The arguments can be of common size or scalar.
 Function File: expinv (x, lambda)
 For each element of x, compute the quantile (the inverse of the CDF) at x of the exponential distribution with mean lambda.
 Function File: exppdf (x, lambda)
 For each element of x, compute the probability density function (PDF) of the exponential distribution with mean lambda.
 Function File: fcdf (x, m, n)
 For each element of x, compute the CDF at x of the F distribution with m and n degrees of freedom, i.e., PROB (F (m, n) <= x).
 Function File: finv (x, m, n)
 For each component of x, compute the quantile (the inverse of the CDF) at x of the F distribution with parameters m and n.
 Function File: fpdf (x, m, n)
 For each element of x, compute the probability density function (PDF) at x of the F distribution with m and n degrees of freedom.
 Function File: gamcdf (x, a, b)
 For each element of x, compute the cumulative distribution
function (CDF) at x of the Gamma distribution with parameters
a and b.
See also gamma, gammaln, gammainc, gampdf, gaminv, gamrnd
 Function File: gaminv (x, a, b)
 For each component of x, compute the quantile (the inverse of
the CDF) at x of the Gamma distribution with parameters a
and b.
See also gamma, gammaln, gammainc, gampdf, gamcdf, gamrnd
 Function File: gampdf (x, a, b)
 For each element of x, return the probability density function
(PDF) at x of the Gamma distribution with parameters a
and b.
See also gamma, gammaln, gammainc, gamcdf, gaminv, gamrnd
 Function File: geocdf (x, p)
 For each element of x, compute the CDF at x of the geometric distribution with parameter p.
 Function File: geoinv (x, p)
 For each element of x, compute the quantile at x of the geometric distribution with parameter p.
 Function File: geopdf (x, p)
 For each element of x, compute the probability density function (PDF) at x of the geometric distribution with parameter p.
 Function File: hygecdf (x, t, m, n)
 Compute the cumulative distribution function (CDF) at x of the hypergeometric distribution with parameters t, m, and n. This is the probability of obtaining not more than x marked items when randomly drawing a sample of size n without replacement from a population of total size t containing m marked items. The parameters t, m, and n must positive integers with m and n not greater than t.
 Function File: hygeinv (x, t, m, n)
 For each element of x, compute the quantile at x of the hypergeometric distribution with parameters t, m, and n. The parameters t, m, and n must positive integers with m and n not greater than t.
 Function File: hygepdf (x, t, m, n)
 Compute the probability density function (PDF) at x of the hypergeometric distribution with parameters t, m, and n. This is the probability of obtaining x marked items when randomly drawing a sample of size n without replacement from a population of total size t containing m marked items. The arguments must be of common size or scalar.
 Function File: kolmogorov_smirnov_cdf (x, tol)
 Return the CDF at x of the KolmogorovSmirnov distribution,
Inf Q(x) = SUM (1)^k exp(2 k^2 x^2) k = Inf
for x > 0. The optional parameter tol specifies the precision up to which the series should be evaluated; the default is tol =eps
.
 Function File: laplace_cdf (x)
 For each element of x, compute the cumulative distribution function (CDF) at x of the Laplace distribution.
 Function File: laplace_inv (x)
 For each element of x, compute the quantile (the inverse of the CDF) at x of the Laplace distribution.
 Function File: laplace_pdf (x)
 For each element of x, compute the probability density function (PDF) at x of the Laplace distribution.
 Function File: logistic_cdf (x)
 For each component of x, compute the CDF at x of the logistic distribution.
 Function File: logistic_inv (x)
 For each component of x, compute the quantile (the inverse of the CDF) at x of the logistic distribution.
 Function File: logistic_pdf (x)
 For each component of x, compute the PDF at x of the logistic distribution.
 Function File: logncdf (x, mu, sigma)
 For each element of x, compute the cumulative distribution function (CDF) at x of the lognormal distribution with parameters mu and sigma. If a random variable follows this distribution, its logarithm is normally distributed with mean mu and standard deviation sigma. Default values are mu = 1, sigma = 1.
 Function File: logninv (x, mu, sigma)
 For each element of x, compute the quantile (the inverse of the
CDF) at x of the lognormal distribution with parameters mu
and sigma. If a random variable follows this distribution, its
logarithm is normally distributed with mean
log (mu)
and variance sigma. Default values are mu = 1, sigma = 1.
 Function File: lognpdf (x, mu, sigma)
 For each element of x, compute the probability density function (PDF) at x of the lognormal distribution with parameters mu and sigma. If a random variable follows this distribution, its logarithm is normally distributed with mean mu and standard deviation sigma. Default values are mu = 1, sigma = 1.
 Function File: nbincdf (x, n, p)
 For each element of x, compute the CDF at x of the Pascal (negative binomial) distribution with parameters n and p. The number of failures in a Bernoulli experiment with success probability p before the nth success follows this distribution.
 Function File: nbininv (x, n, p)
 For each element of x, compute the quantile at x of the Pascal (negative binomial) distribution with parameters n and p. The number of failures in a Bernoulli experiment with success probability p before the nth success follows this distribution.
 Function File: nbinpdf (x, n, p)
 For each element of x, compute the probability density function (PDF) at x of the Pascal (negative binomial) distribution with parameters n and p. The number of failures in a Bernoulli experiment with success probability p before the nth success follows this distribution.
 Function File: normcdf (x, m, s)
 For each element of x, compute the cumulative distribution function (CDF) at x of the normal distribution with mean m and standard deviation s. Default values are m = 0, s = 1.
 Function File: norminv (x, m, s)
 For each element of x, compute the quantile (the inverse of the CDF) at x of the normal distribution with mean m and standard deviation s. Default values are m = 0, s = 1.
 Function File: normpdf (x, m, s)
 For each element of x, compute the probability density function (PDF) at x of the normal distribution with mean m and standard deviation s. Default values are m = 0, s = 1.
 Function File: poisscdf (x, lambda)
 For each element of x, compute the cumulative distribution function (CDF) at x of the Poisson distribution with parameter lambda.
 Function File: poissinv (x, lambda)
 For each component of x, compute the quantile (the inverse of the CDF) at x of the Poisson distribution with parameter lambda.
 Function File: poisspdf (x, lambda)
 For each element of x, compute the probability density function (PDF) at x of the poisson distribution with parameter lambda.
 Function File: tcdf (x, n)
 For each element of x, compute the cumulative distribution function (CDF) at x of the t (Student) distribution with n degrees of freedom, i.e., PROB (t(n) <= x).
 Function File: tinv (x, n)
 For each probability value x, compute the inverse of the cumulative distribution function (CDF) of the t (Student) distribution with degrees of freedom n. This function is analagous to looking in a table for the tvalue of a singletailed distribution.
 Function File: tpdf (x, n)
 For each element of x, compute the probability density function (PDF) at x of the t (Student) distribution with n degrees of freedom.
 Function File: unidcdf (x, v)
 For each element of x, compute the cumulative distribution function (CDF) at x of a univariate discrete distribution which assumes the values in v with equal probability.
 Function File: unidinv (x, v)
 For each component of x, compute the quantile (the inverse of the CDF) at x of the univariate discrete distribution which assumes the values in v with equal probability
 Function File: unidpdf (x, v)
 For each element of x, compute the probability density function (PDF) at x of a univariate discrete distribution which assumes the values in v with equal probability.
 Function File: unifcdf (x, a, b)
 Return the CDF at x of the uniform distribution on [a, b], i.e., PROB (uniform (a, b) <= x). Default values are a = 0, b = 1.
 Function File: unifinv (x, a, b)
 For each element of x, compute the quantile (the inverse of the CDF) at x of the uniform distribution on [a, b]. Default values are a = 0, b = 1.
 Function File: unifpdf (x, a, b)
 For each element of x, compute the PDF at x of the uniform distribution on [a, b]. Default values are a = 0, b = 1.
 Function File: wblcdf (x, scale, shape)
 Compute the cumulative distribution function (CDF) at x of the
Weibull distribution with shape parameter scale and scale
parameter shape, which is
1  exp((x/shape)^scale)
for x >= 0.
 Function File: wblinv (x, scale, shape)
 Compute the quantile (the inverse of the CDF) at x of the Weibull distribution with shape parameter scale and scale parameter shape.
 Function File: wblpdf (x, scale, shape)
 Compute the probability density function (PDF) at x of the
Weibull distribution with shape parameter scale and scale
parameter shape which is given by
scale * shape^(scale) * x^(scale1) * exp((x/shape)^scale)
for x > 0.
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