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
|
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).
For each component of x, compute the quantile (the inverse of the CDF) at x of the Beta distribution with parameters a and b.
For each element of x, returns the PDF at x of the beta distribution with parameters a and b.
For each element of x, compute the CDF at x of the binomial distribution with parameters n and p.
For each element of x, compute the quantile at x of the binomial distribution with parameters n and p.
For each element of x, compute the probability density function (PDF) at x of the binomial distribution with parameters n and p.
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.
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.
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.
For each element of x, compute the cumulative distribution function (CDF) at x of the chisquare distribution with n degrees of freedom.
For each element of x, compute the quantile (the inverse of the CDF) at x of the chisquare distribution with n degrees of freedom.
For each element of x, compute the probability density function (PDF) at x of the chisquare distribution with n degrees of freedom.
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.
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.
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.
For each element of x, compute the cumulative distribution function (CDF) at x of the empirical distribution obtained from the univariate sample 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.
For each element of x, compute the probability density function (PDF) at x of the empirical distribution obtained from the univariate sample data.
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.
For each element of x, compute the quantile (the inverse of the CDF) at x of the exponential distribution with mean lambda.
For each element of x, compute the probability density function (PDF) of the exponential distribution with mean lambda.
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).
For each component of x, compute the quantile (the inverse of the CDF) at x of the F distribution with parameters m and 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.
For each element of x, compute the cumulative distribution function (CDF) at x of the Gamma distribution with parameters a and 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.
For each element of x, return the probability density function (PDF) at x of the Gamma distribution with parameters a and b.
For each element of x, compute the CDF at x of the geometric distribution with parameter p.
For each element of x, compute the quantile at x of the geometric distribution with parameter p.
For each element of x, compute the probability density function (PDF) at x of the geometric distribution with parameter p.
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.
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.
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.
Return the CDF at x of the Kolmogorov-Smirnov distribution,
Inf Q(x) = SUM (-1)^k exp(-2 k^2 x^2) k = -Inffor x > 0.
The optional parameter tol specifies the precision up to which the series should be evaluated; the default is tol =
eps
.
For each element of x, compute the cumulative distribution function (CDF) at x of the Laplace distribution.
For each element of x, compute the quantile (the inverse of the CDF) at x of the Laplace distribution.
For each element of x, compute the probability density function (PDF) at x of the Laplace distribution.
For each component of x, compute the CDF at x of the logistic distribution.
For each component of x, compute the quantile (the inverse of the CDF) at x of the logistic distribution.
For each component of x, compute the PDF at x of the logistic distribution.
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.
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.
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.
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.
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.
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.
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.
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.
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.
For each element of x, compute the cumulative distribution function (CDF) at x of the Poisson distribution with parameter lambda.
For each component of x, compute the quantile (the inverse of the CDF) at x of the Poisson distribution with parameter lambda.
For each element of x, compute the probability density function (PDF) at x of the poisson distribution with parameter lambda.
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).
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 analogous to looking in a table for the t-value of a single-tailed distribution.
For each element of x, compute the probability density function (PDF) at x of the t (Student) distribution with n degrees of freedom.
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.
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
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.
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.
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.
For each element of x, compute the PDF at x of the uniform distribution on [a, b].
Default values are a = 0, b = 1.
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.