Important: The stats package has been deprecated. Use the superseding package Statistics instead.

The following discrete distributions are available:

The following continuous distributions are available:

In the following, the discrete distributions have probability density functions that are evaluated at integral values of x.

The ${\mathrm{binomiald}}_{n,p}$ distribution (binomial distribution) has the probability density function $\left(\genfrac{}{}{0ex}{}{n}{x}\right)p^x{\left(1-p\right)}^{n-x}$. The name binomiald is so chosen in order to distinguish it from the function binomial(). Constraints: x is a non-negative integer no greater than n, n is a positive integer, p is a number between 0 and 1.

The ${\mathrm{discreteuniform}}_{a,b}$ distribution has a probability density function that is equal to zero if $x<a$ or if $b<x$, and equal to $\frac{1}{b-a+1}$ otherwise. Constraints: x is an integer, $a\le b$

The empirical[list_prob] has its probability density function equal to zero if $x<1$ or $\mathrm{nops}\left(\mathrm{list\_prob}\right)<x$ and equal to ${\mathrm{list\_prob}}_x$ otherwise. Constraints: the probabilities must add to 1 exactly.

The ${\mathrm{hypergeometric}}_{\mathrm{N1},\mathrm{N2},n}$, with N1 equal to the size of the success population, N2 equal to the  size of the failure population and n equal to the sample size, has the probability density function $\frac{\left(\genfrac{}{}{0ex}{}{\mathrm{N1}}{x}\right)\left(\genfrac{}{}{0ex}{}{\mathrm{N2}}{n-x}\right)}{\left(\genfrac{}{}{0ex}{}{\mathrm{N1}+\mathrm{N2}}{n}\right)}$. Constraints: $n\le \mathrm{N1}+\mathrm{N2}$.

The ${\mathrm{negativebinomial}}_{n,p}$ distribution has the probability density function equal to

Constraints: x is a non-negative integer no greater than n, n is a positive integer, p is a number between 0 and 1.

The ${\mathrm{poisson}}_{\mathrm{\mu }}$ distribution has the probability density function exp(-mu)*mu^x/x!

For the continuous distributions, the parameter x takes a real value.

The ${\mathrm{\beta }}_{\mathrm{\&nu;1},\mathrm{\&nu;2}}$ distribution has the probability density function

Constraints: nu1, nu2 are positive integers.

The ${\mathrm{cauchy}}_{a,b}$ distribution has the probability density function $\frac{1}{\mathrm{\pi }b\left(1+\frac{{\left(x-a\right)}^2}{b^2}\right)},0<b$.

The ${\mathrm{chisquare}}_{\mathrm{\nu }}$ distribution has the probability density function

Constraint: nu is a positive integer.

The ${\mathrm{exponential}}_{\mathrm{\alpha },a}$ distribution (exponential distribution) has the probability density function equal to  $\mathrm{\alpha }{\&ExponentialE;}^{-\mathrm{\alpha }\left(x-a\right)}$ if $a\le x$ and equal to zero if $x<a$. Constraint: alpha is a non-negative real number. Default: $a=0$.

The ${\mathrm{fratio}}_{\mathrm{\&nu;1},\mathrm{\&nu;2}}$ distribution has the probability density function

This distribution is also known as the Fisher F distribution and the variance ratio distribution. Constraints: nu1, nu2 are positive integers.

The ${\mathrm{\gamma }}_{a,b}$ distribution gamma distribution has the probability density function $\frac{x^{a-1}{\&ExponentialE;}^{-\frac{x}{b}}}{\mathrm{\Gamma }\left(a\right)b^a},0<x,0<a,0<b$. The parameter b, if absent, defaults to the value $1$.

The ${\mathrm{laplaced}}_{a,b}$ distribution has the probability density function $\frac{{\&ExponentialE;}^{-\frac{\left|x-a\right|}{b}}}{2b}$, $0<b$. The name laplaced is so chosen to distinguish it from the laplace() function.

The ${\mathrm{logistic}}_{a,b}$ distribution has the probability density function

The ${\mathrm{lognormal}}_{\mathrm{\mu },\mathrm{\sigma }}$ has the probability density function

The parameter mu has the default value $0$ and the parameter sigma has the default value $1$. Constraint: sigma cannot be 0. See also the normald distribution.

The ${\mathrm{normald}}_{\mathrm{\mu },\mathrm{\sigma }}$ distribution has the probability density function

The parameter mu has the default value $0$ and the parameter sigma has the default value $1$. Note that sigma is the standard deviation and not the variance. Constraint: sigma must be positive.

The ${\mathrm{studentst}}_{\mathrm{\nu }}$ distribution has the probability density function

Constraint: nu is a positive integer.

The ${\mathrm{uniform}}_{a,b}$ distribution has the probability density function equal to $\frac{1}{b-a}$ if $a<=x<=b$, and to  $0$ otherwise. The value of b defaults to $1+a$. The value of a defaults to 0. Constraint: $a<b$.

The ${\mathrm{weibull}}_{a,b}$ distribution has the probability density function

$\mathrm{stats}\left[\mathrm{statevalf},\mathrm{pf},\mathrm{poisson}\left[3\right]\right]\left(2\right)$

$0.2240418077$

$\mathrm{stats}\left[\mathrm{statevalf},\mathrm{icdf},\mathrm{normald}\right]\left(0.56\right)$

$0.1509692155$

$\mathrm{stats}\left[\mathrm{random},\mathrm{\gamma }\left[3,1\right]\right]\left(3\right)$

$2.482561473,0.5545542660,2.632923698$