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
|
Chi-Square 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
|
Log-Normal 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 Kolmogorov-Smirnov 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 n-th 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 n-th 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 n-th 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 t-value of a single-tailed 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^(scale-1) * exp(-(x/shape)^scale)
for x > 0.
ISBN 095461206X | GNU Octave Manual Version 3 | See the print edition |