Help language development. Donate to The Perl Foundation
[](https://github.com/frithnanth/raku-Math-Libgsl-RandomDistribution/actions)
NAME
====
Math::Libgsl::RandomDistribution - An interface to libgsl, the Gnu Scientific Library - Random Number Distributions
SYNOPSIS
========
```perl6
use Math::Libgsl::Random;
use Math::Libgsl::RandomDistribution;
my Math::Libgsl::Random $r .= new;
say poisson($r, 3) for ^10;
```
DESCRIPTION
===========
Math::Libgsl::RandomDistribution is an interface to the Random Number Distributions section of libgsl, the Gnu Scientific Library.
### gaussian(Math::Libgsl::Random $r, Num() $sigma --> Num)
This function returns a Gaussian random variate, with mean zero and standard deviation $sigma.
### gaussian-pdf(Num() $x, Num() $sigma --> Num)
This function computes the probability density at $x for a Gaussian distribution with standard deviation $sigma.
### gaussian-ziggurat(Math::Libgsl::Random $r, Num() $sigma --> Num)
### gaussian-ratio-method(Math::Libgsl::Random $r, Num() $sigma --> Num)
This function computes a Gaussian random variate using the alternative Marsaglia-Tsang ziggurat and Kinderman-Monahan-Leva ratio methods.
### ugaussian(Math::Libgsl::Random $r --> Num)
### ugaussian-pdf(Num() $x --> Num)
### ugaussian-ratio-method(Math::Libgsl::Random $r --> Num)
These functions compute results for the unit Gaussian distribution. They are equivalent to the functions above with $sigma = 1.
### gaussian-P(Num() $x, Num() $sigma --> Num)
### gaussian-Q(Num() $x, Num() $sigma --> Num)
### gaussian-Pinv(Num() $P, Num() $sigma --> Num)
### gaussian-Qinv(Num() $Q, Num() $sigma --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses.
### ugaussian-P(Num() $x --> Num)
### ugaussian-Q(Num() $x --> Num)
### ugaussian-Pinv(Num() $P --> Num)
### ugaussian-Qinv(Num() $Q --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the unit Gaussian distribution.
### gaussian-tail(Math::Libgsl::Random $r, Num() $a where * > 0, Num() $sigma --> Num)
This function provides random variates from the upper tail of a Gaussian distribution with standard deviation $sigma.
### gaussian-tail-pdf(Num() $x, Num() $a where * > 0, Num() $sigma --> Num)
This function computes the probability density p(x) at $x for a Gaussian tail distribution with standard deviation $sigma and lower limit $a.
### ugaussian-tail(Math::Libgsl::Random $r, Num() $a where * > 0 --> Num)
### ugaussian-tail-pdf(Num() $x, Num() $a where * > 0 --> Num)
These functions compute results for the tail of a unit Gaussian distribution.
### bivariate-gaussian(Math::Libgsl::Random $r, Num() $sigma-x, Num() $sigma-y, Num() $rho where -1 < * < 1 --> List)
This function generates a pair of correlated Gaussian variates, with mean zero, correlation coefficient $rho and standard deviations $sigma_x and $sigma_y. The function returns two Num values: the Gauusian correlates along the x and y directions.
### bivariate-gaussian-pdf(Num() $x, Num() $y, Num() $sigma-x, Num() $sigma-y, Num() $rho where -1 < * < 1 --> Num)
This function computes the probability density p(x, y) at ($x, $y) for a bivariate Gaussian distribution with standard deviations $sigma_x, $sigma_y and correlation coefficient $rho.
### multivariate-gaussian(Math::Libgsl::Random $r, Math::Libgsl::Vector $mu, Math::Libgsl::Matrix $L where { $L.matrix.size1 == $L.matrix.size2 && $L.matrix.size1 == $mu.vector.size } --> Math::Libgsl::Vector)
This function generates a random vector satisfying the k-dimensional multivariate Gaussian distribution with mean μ and variance-covariance matrix Σ. On input, the k-vector μ is given in $mu, and the Cholesky factor of the k-by-k matrix Σ = LT(L) is given in the lower triangle of $L, as output from Math::Libgsl::LinearAlgebra::cholesky-decomp(). The function returns the random vector as a Math::Libgsl::Vector object.
### multivariate-gaussian-pdf(Math::Libgsl::Vector $x, Math::Libgsl::Vector $mu where *.vector.size == $x.vector.size, Math::Libgsl::Matrix $L where { $L.matrix.size1 == $L.matrix.size2 && $L.matrix.size1 == $mu.vector.size } --> Num)
### multivariate-gaussian-log-pdf(Math::Libgsl::Vector $x, Math::Libgsl::Vector $mu where *.vector.size == $x.vector.size, Math::Libgsl::Matrix $L where { $L.matrix.size1 == $L.matrix.size2 && $L.matrix.size1 == $mu.vector.size } --> Num)
These functions compute p(x) or log p(x) at the point $x, using mean vector $mu and variance-covariance matrix specified by its Cholesky factor $L.
### multivariate-gaussian-mean(Math::Libgsl::Matrix $X --> Math::Libgsl::Vector)
Given a set of n samples Xⱼ from a k-dimensional multivariate Gaussian distribution, this function computes the maximum likelihood estimate of the mean of the distribution. The function returns the maximum likelihood estimate as a Math::Libgsl::Vector object.
### multivariate-gaussian-vcov(Math::Libgsl::Matrix $X --> Math::Libgsl::Matrix)
Given a set of n samples Xⱼ from a k-dimensional multivariate Gaussian distribution, this function computes the maximum likelihood estimate of the variance-covariance matrix of the distribution. The function returns the maximum likelihood estimate of the variance-covariance matrix as a Math::Libgsl::Matrix object.
### exponential(Math::Libgsl::Random $r, Num() $mu --> Num)
This function returns a random variate from the exponential distribution with mean $mu.
### exponential-pdf(Num() $x, Num() $mu --> Num)
This function computes the probability density p(x) at $x for an exponential distribution with mean $mu.
### exponential-P(Num() $x, Num() $mu --> Num)
### exponential-Q(Num() $x, Num() $mu --> Num)
### exponential-Pinv(Num() $P, Num() $mu --> Num)
### exponential-Qinv(Num() $Q, Num() $mu --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the exponential distribution with mean $mu.
### laplace(Math::Libgsl::Random $r, Num() $a --> Num)
This function returns a random variate from the Laplace distribution with width $a.
### laplace-pdf(Num() $x, Num() $a --> Num)
This function computes the probability density p(x) at $x for a Laplace distribution with width $a.
### laplace-P(Num() $x, Num() $a --> Num)
### laplace-Q(Num() $x, Num() $a --> Num)
### laplace-Pinv(Num() $P, Num() $a --> Num)
### laplace-Qinv(Num() $Q, Num() $a --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Laplace distribution with width $a.
### exppow(Math::Libgsl::Random $r, Num() $a, Num() $b --> Num)
This function returns a random variate from the exponential power distribution with scale parameter $a and exponent $b.
### exppow-pdf(Num() $x, Num() $a, Num() $b --> Num)
This function computes the probability density p(x) at $x for an exponential power distribution with scale parameter $a and exponent $b.
### exppow-P(Num() $x, Num() $a, Num() $b --> Num)
### exppow-Q(Num() $x, Num() $a, Num() $b --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) for the exponential power distribution with parameters $a and $b.
### cauchy(Math::Libgsl::Random $r, Num() $a --> Num)
This function returns a random variate from the Cauchy distribution with scale parameter $a.
### cauchy-pdf(Num() $x, Num() $a --> Num)
This function computes the probability density p(x) at $x for a Cauchy distribution with scale parameter $a.
### cauchy-P(Num() $x, Num() $a --> Num)
### cauchy-Q(Num() $x, Num() $a --> Num)
### cauchy-Pinv(Num() $P, Num() $a --> Num)
### cauchy-Qinv(Num() $Q, Num() $a --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Cauchy distribution with scale parameter $a.
### rayleigh(Math::Libgsl::Random $r, Num() $sigma --> Num)
This function returns a random variate from the Rayleigh distribution with scale parameter $sigma.
### rayleigh-pdf(Num() $x, Num() $sigma --> Num)
This function computes the probability density p(x) at $x for a Rayleigh distribution with scale parameter $sigma.
### rayleigh-P(Num() $x, Num() $sigma --> Num)
### rayleigh-Q(Num() $x, Num() $sigma --> Num)
### rayleigh-Pinv(Num() $P, Num() $sigma --> Num)
### rayleigh-Qinv(Num() $Q, Num() $sigma --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Rayleigh distribution with scale parameter $sigma.
### rayleigh-tail(Math::Libgsl::Random $r, Num() $a, Num() $sigma --> Num)
This function returns a random variate from the tail of the Rayleigh distribution with scale parameter $sigma and a lower limit of $a.
### rayleigh-tail-pdf(Num() $x, Num() $a, Num() $sigma --> Num)
This function computes the probability density p(x) at $x for a Rayleigh tail distribution with scale parameter $sigma and lower limit $a.
### landau(Math::Libgsl::Random $r --> Num)
This function returns a random variate from the Landau distribution.
### landau-pdf(Num() $x --> Num)
This function computes the probability density p(x) at $x for the Landau distribution.
### levy(Math::Libgsl::Random $r, Num() $c, Num() $alpha where 0 < * ≤ 2 --> Num)
This function returns a random variate from the Levy symmetric stable distribution with scale $c and exponent $alpha.
### levy-skew(Math::Libgsl::Random $r, Num() $c, Num() $alpha where 0 < * ≤ 2, Num() $beta --> Num)
This function returns a random variate from the Levy skew stable distribution with scale $c, exponent $alpha and skewness parameter $beta.
### gamma(Math::Libgsl::Random $r, Num() $a, Num() $b --> Num)
This function returns a random variate from the gamma distribution.
### gamma-knuth(Math::Libgsl::Random $r, Num() $a, Num() $b --> Num)
This function returns a gamma variate using the algorithms from Knuth.
### gamma-pdf(Num() $x, Num() $a, Num() $b --> Num)
This function computes the probability density p(x) at $x for a gamma distribution with parameters $a and $b.
### gamma-P(Num() $x, Num() $a, Num() $b --> Num)
### gamma-Q(Num() $x, Num() $a, Num() $b --> Num)
### gamma-Pinv(Num() $P, Num() $a, Num() $b --> Num)
### gamma-Qinv(Num() $Q, Num() $a, Num() $b --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the gamma distribution with parameters $a and $b.
### flat(Math::Libgsl::Random $r, Num() $a, Num() $b --> Num)
This function returns a random variate from the flat (uniform) distribution from $a to $b.
### flat-pdf(Num() $x, Num() $a, Num() $b --> Num)
This function computes the probability density p(x) at $x for a uniform distribution from $a to $b.
### flat-P(Num() $x, Num() $a, Num() $b --> Num)
### flat-Q(Num() $x, Num() $a, Num() $b --> Num)
### flat-Pinv(Num() $P, Num() $a, Num() $b --> Num)
### flat-Qinv(Num() $Q, Num() $a, Num() $b --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for a uniform distribution from $a to $b.
### lognormal(Math::Libgsl::Random $r, Num() $zeta, Num() $sigma --> Num)
This function returns a random variate from the lognormal distribution.
### lognormal-pdf(Num() $x, Num() $zeta, Num() $sigma --> Num)
This function computes the probability density p(x) at $x for a lognormal distribution with parameters $zeta and $sigma.
### lognormal-P(Num() $x, Num() $zeta, Num() $sigma --> Num)
### lognormal-Q(Num() $x, Num() $zeta, Num() $sigma --> Num)
### lognormal-Pinv(Num() $P, Num() $zeta, Num() $sigma --> Num)
### lognormal-Qinv(Num() $Q, Num() $zeta, Num() $sigma --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the lognormal distribution with parameters $zeta and $sigma.
### chisq(Math::Libgsl::Random $r, Num() $nu --> Num)
This function returns a random variate from the chi-squared distribution with $nu degrees of freedom.
### chisq-pdf(Num() $x where * ≥ 0, Num() $nu --> Num)
This function computes the probability density p(x) at $x for a chi-squared distribution with $nu degrees of freedom.
### chisq-P(Num() $x where * ≥ 0, Num() $nu --> Num)
### chisq-Q(Num() $x where * ≥ 0, Num() $nu --> Num)
### chisq-Pinv(Num() $P, Num() $nu --> Num)
### chisq-Qinv(Num() $Q, Num() $nu --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the chi-squared distribution with $nu degrees of freedom.
### fdist(Math::Libgsl::Random $r, Num() $nu1, Num() $nu2 --> Num)
This function returns a random variate from the F-distribution with degrees of freedom $nu1 and $nu2.
### fdist-pdf(Num() $x where * ≥ 0, Num() $nu1, Num() $nu2 --> Num)
This function computes the probability density p(x) at $x for an F-distribution with $nu1 and $nu2 degrees of freedom.
### fdist-P(Num() $x where * ≥ 0, Num() $nu1, Num() $nu2 --> Num)
### fdist-Q(Num() $x where * ≥ 0, Num() $nu1, Num() $nu2 --> Num)
### fdist-Pinv(Num() $P, Num() $nu1, Num() $nu2 --> Num)
### fdist-Qinv(Num() $Q, Num() $nu1, Num() $nu2 --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the F-distribution with $nu1 and $nu2 degrees of freedom.
### tdist(Math::Libgsl::Random $r, Num() $nu --> Num)
This function returns a random variate from the t-distribution.
### tdist-pdf(Num() $x, Num() $nu --> Num)
This function computes the probability density p(x) at $x for a t-distribution with $nu degrees of freedom.
### tdist-P(Num() $x, Num() $nu --> Num)
### tdist-Q(Num() $x, Num() $nu --> Num)
### tdist-Pinv(Num() $P, Num() $nu --> Num)
### tdist-Qinv(Num() $Q, Num() $nu --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the t-distribution with $nu degrees of freedom.
### beta(Math::Libgsl::Random $r, Num() $a, Num() $b --> Num)
This function returns a random variate from the beta distribution.
### beta-pdf(Num() $x, Num() $a, Num() $b --> Num)
This function computes the probability density p(x) at $x for a beta distribution with parameters $a and $b.
### beta-P(Num() $x, Num() $a, Num() $b --> Num)
### beta-Q(Num() $x, Num() $a, Num() $b --> Num)
### beta-Pinv(Num() $P, Num() $a, Num() $b --> Num)
### beta-Qinv(Num() $Q, Num() $a, Num() $b --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the beta distribution with parameters $a and $b.
### logistic(Math::Libgsl::Random $r, Num() $a --> Num)
This function returns a random variate from the logistic distribution.
### logistic-pdf(Num() $x, Num() $a --> Num)
This function computes the probability density p(x) at $x for a logistic distribution with scale parameter $a.
### logistic-P(Num() $x, Num() $a --> Num)
### logistic-Q(Num() $x, Num() $a --> Num)
### logistic-Pinv(Num() $P, Num() $a --> Num)
### logistic-Qinv(Num() $Q, Num() $a --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the logistic distribution with scale parameter $a.
### pareto(Math::Libgsl::Random $r, Num() $a, Num() $b --> Num)
This function returns a random variate from the Pareto distribution of order $a and scale $b.
### pareto-pdf(Num() $x, Num() $a, Num() $b where { $x ≥ $b } --> Num)
This function computes the probability density p(x) at $x for a Pareto distribution with exponent $a and scale $b.
### pareto-P(Num() $x, Num() $a, Num() $b where { $x ≥ $b } --> Num)
### pareto-Q(Num() $x, Num() $a, Num() $b where { $x ≥ $b } --> Num)
### pareto-Pinv(Num() $P, Num() $a, Num() $b --> Num)
### pareto-Qinv(Num() $Q, Num() $a, Num() $b --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Pareto distribution with exponent $a and scale $b.
### d2dir(Math::Libgsl::Random $r --> List)
### d2dir-trig-method(Math::Libgsl::Random $r --> List)
This function returns a random direction vector v = (x, y) in two dimensions. The return value is a List of two Num(s): the x and y components of the 2D vector.
### d3dir(Math::Libgsl::Random $r --> List)
This function returns a random direction vector v = (x, y, z) in three dimensions. The return value is a List of three Num(s): the x, y, and z components of the 3D vector.
### dndir(Math::Libgsl::Random $r, Int $n --> List)
This function returns a random direction vector v = (x 1 , x 2 , . . . , x n ) in $n dimensions. The return value is a List of $n Num(s): the components of the n-D vector.
### weibull(Math::Libgsl::Random $r, Num() $a, Num() $b --> Num)
This function returns a random variate from the Weibull distribution.
### weibull-pdf(Num() $x where $x ≥ 0, Num() $a, Num() $b --> Num)
This function computes the probability density p(x) at $x for a Weibull distribution with scale $a and exponent $b.
### weibull-P(Num() $x where $x ≥ 0, Num() $a, Num() $b --> Num)
### weibull-Q(Num() $x where $x ≥ 0, Num() $a, Num() $b --> Num)
### weibull-Pinv(Num() $P, Num() $a, Num() $b --> Num)
### weibull-Qinv(Num() $Q, Num() $a, Num() $b --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Weibull distribution with scale $a and exponent $b.
### gumbel1(Math::Libgsl::Random $r, Num() $a, Num() $b --> Num)
This function returns a random variate from the Type-1 Gumbel distribution.
### gumbel1-pdf(Num() $x, Num() $a, Num() $b --> Num)
This function computes the probability density p(x) at $x for a Type-1 Gumbel distribution with parameters $a and $b.
### gumbel1-P(Num() $x, Num() $a, Num() $b --> Num)
### gumbel1-Q(Num() $x, Num() $a, Num() $b --> Num)
### gumbel1-Pinv(Num() $P, Num() $a, Num() $b --> Num)
### gumbel1-Qinv(Num() $Q, Num() $a, Num() $b --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Type-1 Gumbel distribution with parameters $a and $b.
### gumbel2(Math::Libgsl::Random $r, Num() $a, Num() $b --> Num)
This function returns a random variate from the Type-2 Gumbel distribution.
### gumbel2-pdf(Num() $x where * > 0, Num() $a, Num() $b --> Num)
This function computes the probability density p(x) at $x for a Type-2 Gumbel distribution with parameters $a and $b.
### gumbel2-P(Num() $x where * > 0, Num() $a, Num() $b --> Num)
### gumbel2-Q(Num() $x where * > 0, Num() $a, Num() $b --> Num)
### gumbel2-Pinv(Num() $P, Num() $a, Num() $b --> Num)
### gumbel2-Qinv(Num() $Q, Num() $a, Num() $b --> Num)
These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Type-2 Gumbel distribution with parameters $a and $b.
### dirichlet(Math::Libgsl::Random $r, Int $K, @alpha where *.all > 0 --> List)
This function returns an array of K random variates as a List of Num(s) from a Dirichlet distribution of order K-1.
### dirichlet-pdf(Int $K, @alpha where *.all > 0, @theta where *.all ≥ 0 --> Num)
This function computes the probability density p(θ₁, …, θₖ) at theta[K] for a Dirichlet distribution with parameters alpha[K].
### dirichlet-lnpdf(Int $K, @alpha where *.all > 0, @theta where *.all ≥ 0 --> Num)
This function computes the logarithm of the probability density p(θ₁, …, θₖ) at theta[K] for a Dirichlet distribution with parameters alpha[K].
### poisson(Math::Libgsl::Random $r, Num() $mu --> UInt)
This function returns a random integer from the Poisson distribution with mean $mu.
### poisson-pdf(UInt $k, Num() $mu --> Num)
This function computes the probability p(k) of obtaining $k from a Poisson distribution with mean $mu.
### poisson-P(UInt $k, Num() $mu --> Num)
### poisson-Q(UInt $k, Num() $mu --> Num)
These functions compute the cumulative distribution functions P(k), Q(k) for the Poisson distribution with parameter $mu.
### bernoulli(Math::Libgsl::Random $r, Num() $p --> Int)
This function returns either 0 or 1, the result of a Bernoulli trial with probability $p.
### bernoulli-pdf(UInt $k, Num() $p --> Num)
This function computes the probability p(k) of obtaining $k from a Bernoulli distribution with probability parameter $p.
### binomial(Math::Libgsl::Random $r, Num() $p, UInt $n --> Int)
This function returns a random integer from the binomial distribution, the number of successes in $n independent trials with probability $p.
### binomial-pdf(UInt $k, Num() $p, UInt $n where * ≥ $k --> Num)
This function computes the probability p(k) of obtaining $k from a binomial distribution with parameters $p and $n.
### binomial-P(UInt $k, Num() $p, UInt $n where * ≥ $k --> Num)
### binomial-Q(UInt $k, Num() $p, UInt $n where * ≥ $k --> Num)
These functions compute the cumulative distribution functions P (k), Q(k) for the binomial distribution with parameters $p and $n.
### multinomial(Math::Libgsl::Random $r, Int $K, UInt $N, *@p where { @p.all ~~ Numeric } --> List)
This function returns a random sample from the multinomial distribution formed by $N trials from an underlying distribution p[K] as a List of UInt(s).
### multinomial-pdf(Int $K, @p where { @p.all ~~ Numeric }, *@n where { @n.all ~~ UInt } --> Num)
This function computes the probability P(n₁, n₂, …, nₖ) of sampling n[K] from a multinomial distribution with parameters p[K].
### multinomial-lnpdf(Int $K, @p where { @p.all ~~ Numeric }, *@n where { @n.all ~~ UInt } --> Num)
This function computes the logarithm of the probability P(n₁, n₂, …, nₖ) for the multinomial distribution with parameters p[K].
### negative-binomial(Math::Libgsl::Random $r, Num() $p, Num() $n --> UInt)
This function returns a random integer from the negative binomial distribution.
### negative-binomial-pdf(UInt $k, Num() $p, Num() $n --> Num)
This function computes the probability p(k) of obtaining $k from a negative binomial distribution with parameters $p and $n.
### negative-binomial-P(UInt $k, Num() $p, Num() $n --> Num)
### negative-binomial-Q(UInt $k, Num() $p, Num() $n --> Num)
These functions compute the cumulative distribution functions P(k), Q(k) for the negative binomial distribution with parameters $p and $n.
### pascal(Math::Libgsl::Random $r, Num() $p, UInt $n --> UInt)
This function returns a random integer from the Pascal distribution.
### pascal-pdf(UInt $k, Num() $p, UInt $n --> Num)
This function computes the probability p(k) of obtaining $k from a Pascal distribution with parameters $p and $n.
### pascal-P(UInt $k, Num() $p, UInt $n --> Num)
### pascal-Q(UInt $k, Num() $p, UInt $n --> Num)
These functions compute the cumulative distribution functions P(k), Q(k) for the Pascal distribution with parameters $p and $n.
### geometric(Math::Libgsl::Random $r, Num() $p --> UInt)
This function returns a random integer from the geometric distribution, the number of independent trials with probability $p until the first success.
### geometric-pdf(UInt $k where * ≥ 1, Num() $p --> Num)
This function computes the probability p(k) of obtaining $k from a geometric distribution with probability parameter $p.
### geometric-P(UInt $k where * ≥ 1, Num() $p --> Num)
### geometric-Q(UInt $k where * ≥ 1, Num() $p --> Num)
These functions compute the cumulative distribution functions P(k), Q(k) for the geometric distribution with parameter $p.
### hypergeometric(Math::Libgsl::Random $r, UInt $n1, UInt $n2, UInt $t --> UInt)
This function returns a random integer from the hypergeometric distribution.
### hypergeometric-pdf(UInt $k, UInt $n1, UInt $n2, UInt $t --> Num)
This function computes the probability p(k) of obtaining $k from a hypergeometric distribution with parameters $n1, $n2, $t.
### hypergeometric-P(UInt $k, UInt $n1, UInt $n2, UInt $t --> Num)
### hypergeometric-Q(UInt $k, UInt $n1, UInt $n2, UInt $t --> Num)
These functions compute the cumulative distribution functions P(k), Q(k) for the hypergeometric distribution with parameters $n1, $n2 and $t.
### logarithmic(Math::Libgsl::Random $r, Num() $p --> UInt)
This function returns a random integer from the logarithmic distribution.
### logarithmic-pdf(UInt $k where * ≥ 1, Num() $p --> Num)
This function computes the probability p(k) of obtaining $k from a logarithmic distribution with probability parameter $p.
### wishart(Math::Libgsl::Random $r, Num() $n, Math::Libgsl::Matrix $L where { $L.matrix.size1 == $L.matrix.size2 && $n ≤ $L.matrix.size1 - 1 } --> Math::Libgsl::Matrix)
This function returns a random symmetric p-by-p matrix from the Wishart distribution as a Math::Libgsl::Matrix object.
### wishart-pdf(Math::Libgsl::Matrix $X where { $X.matrix.size1 == $X.matrix.size2 }, Math::Libgsl::Matrix $L-X where { $L-X.matrix.size1 == $L-X.matrix.size2 }, Num() $n where * > $X.matrix.size1 - 1, Math::Libgsl::Matrix $L where { $L.matrix.size1 == $L.matrix.size2 && $X.matrix.size1 == $L.matrix.size1 && $L-X.matrix.size1 == $L.matrix.size1 } --> Num)
### wishart-log-pdf(Math::Libgsl::Matrix $X where { $X.matrix.size1 == $X.matrix.size2 }, Math::Libgsl::Matrix $L-X where { $L-X.matrix.size1 == $L-X.matrix.size2 }, Num() $n where * > $X.matrix.size1 - 1, Math::Libgsl::Matrix $L where { $L.matrix.size1 == $L.matrix.size2 && $X.matrix.size1 == $L.matrix.size1 && $L-X.matrix.size1 == $L.matrix.size1 } --> Num)
These functions return p(X) or log p(X) for the p-by-p matrix $X, whose Cholesky factor is specified in $L-X. The degrees of freedom is given by $n, the Cholesky factor of the scale matrix V is specified in $L.
### shuffle(Math::Libgsl::Random $r, @base --> List)
This function randomly shuffles the order of the elements of the array @base and returns them as a List.
### choose(Math::Libgsl::Random $r, Int $k, @src where *.elems ≥ $k --> List)
This function returns the list of $k objects taken randomly from the elements of the array @src.
### sample(Math::Libgsl::Random $r, Int $k, @src --> List)
This function is like choose() but samples $k items from the original array of n items @src with replacement, so the same object can appear more than once in the output.
Class Math::Libgsl::RandomDistribution::Discrete
------------------------------------------------
This probability distribution needs a lookup table for the discrete random number generator, so it's implemented as a class, which hides the implementation details.
```perl6
use Math::Libgsl::RandomDistribution;
use Math::Libgsl::Random;
my Int $size = 3;
my @probability = .59, .4, .01;
my Math::Libgsl::Random $r .= new;
my Math::Libgsl::RandomDistribution::Discrete $d .= new: :$size, :@probability;
say "Using probability values: { $d.probability }";
say $d.discrete($r) for ^10;
say $d.discrete-pdf(2);
```
### new(Int() :$size, :@probability where *.all > 0)
Creates the lookup table for the discrete random number generator. The array @probability contains the probabilities of the discrete events.
### discrete(Math::Libgsl::Random $r --> Int)
This method returns one discrete random number.
### discrete-pdf(Int $k --> Num)
This method returns the probability P[k] of observing the variable $k.
C Library Documentation
=======================
For more details on libgsl see [https://www.gnu.org/software/gsl/](https://www.gnu.org/software/gsl/). The excellent C Library manual is available here [https://www.gnu.org/software/gsl/doc/html/index.html](https://www.gnu.org/software/gsl/doc/html/index.html), or here [https://www.gnu.org/software/gsl/doc/latex/gsl-ref.pdf](https://www.gnu.org/software/gsl/doc/latex/gsl-ref.pdf) in PDF format.
Prerequisites
=============
This module requires the libgsl library to be installed. Please follow the instructions below based on your platform:
Debian Linux and Ubuntu 20.04
-----------------------------
sudo apt install libgsl23 libgsl-dev libgslcblas0
That command will install libgslcblas0 as well, since it's used by the GSL.
Ubuntu 18.04
------------
libgsl23 and libgslcblas0 have a missing symbol on Ubuntu 18.04. I solved the issue installing the Debian Buster version of those three libraries:
* [http://http.us.debian.org/debian/pool/main/g/gsl/libgslcblas0_2.5+dfsg-6_amd64.deb](http://http.us.debian.org/debian/pool/main/g/gsl/libgslcblas0_2.5+dfsg-6_amd64.deb)
* [http://http.us.debian.org/debian/pool/main/g/gsl/libgsl23_2.5+dfsg-6_amd64.deb](http://http.us.debian.org/debian/pool/main/g/gsl/libgsl23_2.5+dfsg-6_amd64.deb)
* [http://http.us.debian.org/debian/pool/main/g/gsl/libgsl-dev_2.5+dfsg-6_amd64.deb](http://http.us.debian.org/debian/pool/main/g/gsl/libgsl-dev_2.5+dfsg-6_amd64.deb)
Installation
============
To install it using zef (a module management tool):
$ zef install Math::Libgsl::RandomDistribution
AUTHOR
======
Fernando Santagata <[email protected]>
COPYRIGHT AND LICENSE
=====================
Copyright 2020 Fernando Santagata
This library is free software; you can redistribute it and/or modify it under the Artistic License 2.0.