[![Actions Status](https://github.com/frithnanth/raku-Math-Libgsl-RandomDistribution/workflows/test/badge.svg)](https://github.com/frithnanth/raku-Math-Libgsl-RandomDistribution/actions) ![2D Random Walk](examples/2Drandomwalk.svg "2D Random Walk") 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 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.