GSL.Random.Dist

Random number distributions. Functions for generating random variates and computing their probability distributions.

The Gaussian Distribution

General

gaussianPdf :: Double -> Double -> Double

gaussianPdf x sigma computes the probabililty density p(x) for a Gaussian distribution with mean 0 and standard deviation sigma.

gaussianP :: Double -> Double -> Double

gaussianP x sigma computes the cumulative distribution function P(x) for a Gaussian distribution with mean 0 and standard deviation sigma.

gaussianQ :: Double -> Double -> Double

gaussianQ x sigma computes the cumulative distribution function Q(x) for a Gaussian distribution with mean 0 and standard deviation sigma.

gaussianPInv :: Double -> Double -> Double

gaussianPInv p sigma computes the inverse of the cumulative distribution function of a Gaussian distribution with mean 0 and standard deviation sigma. It returns x such that P(x) = p.

gaussianQInv :: Double -> Double -> Double

gaussianPInv q sigma computes the inverse of the cumulative distribution function of a Gaussian distribution with mean 0 and standard deviation sigma. It returns x such that Q(x) = q.

getGaussian :: RNG -> Double -> IO Double

getGaussian r sigma gets a normal random variable with mean 0 and standard deviation sigma. This uses the Box-Mueller algorithm.

getGaussianZiggurat :: RNG -> Double -> IO Double

getGaussianZiggurat r sigma gets a normal random variable with mean 0 and standard deviation sigma. This uses the Marsaglia-Tsang ziggurat algorithm.

getGaussianRatioMethod :: RNG -> Double -> IO Double

getGaussianRatioMethod r sigma gets a normal random variable with mean 0 and standard deviation sigma. This uses the Kinderman-Monahan-Leva ratio method.

Unit Variance

ugaussianPdf :: Double -> Double

ugaussianPdf x computes the probabililty density p(x) for a Gaussian distribution with mean 0 and standard deviation 1.

ugaussianP :: Double -> Double

ugaussianP x computes the cumulative distribution function P(x) for a Gaussian distribution with mean 0 and standard deviation 1.

ugaussianQ :: Double -> Double

ugaussianQ x computes the cumulative distribution function Q(x) for a Gaussian distribution with mean 0 and standard deviation 1.

ugaussianPInv :: Double -> Double

ugaussianPInv p computes the inverse of the cumulative distribution function of a Gaussian distribution with mean 0 and standard deviation 1. It returns x such that P(x) = p.

ugaussianQInv :: Double -> Double

ugaussianPInv q computes the inverse of the cumulative distribution function of a Gaussian distribution with mean 0 and standard deviation 1. It returns x such that Q(x) = q.

getUGaussian :: RNG -> IO Double

getUGaussian r gets a normal random variable with mean 0 and standard deviation 1. This uses the Box-Mueller algorithm.

getUGaussianRatioMethod :: RNG -> IO Double

getUGaussianRatioMethod r gets a normal random variable with mean 0 and standard deviation 1. This uses the Kinderman-Monahan-Leva ratio method.

The Flat (Uniform) Distribution

flatPdf :: Double -> Double -> Double -> Double

flatPdf x a b computes the probability density p(x) at x for a uniform distribution from a to b.

flatP :: Double -> Double -> Double -> Double

flatP x a b computes the cumulative distribution function P(x).

flatQ :: Double -> Double -> Double -> Double

flatQ x a b computes the cumulative distribution function Q(x).

flatPInv :: Double -> Double -> Double -> Double

flatPInv p a b computes the inverse of the cumulative distribution and returns x so that function P(x) = p.

flatQInv :: Double -> Double -> Double -> Double

flatQInv q a b computes the inverse of the cumulative distribution and returns x so that function Q(x) = q.

getFlat :: RNG -> Double -> Double -> IO Double

getFlat r a b gets a value uniformly chosen in [a,b).

The Exponential Distribution

exponentialPdf :: Double -> Double -> Double

exponentialPdf x mu computes the density at x of an exponential with mean mu.

exponentialP :: Double -> Double -> Double

exponentialQ :: Double -> Double -> Double

exponentialPInv :: Double -> Double -> Double

exponentialQInv :: Double -> Double -> Double

getExponential :: RNG -> Double -> IO Double

getExponential r mu gets a random exponential with mean mu.

The Levy alpha-Stable Distributions

getLevy :: RNG -> Double -> Double -> IO Double

getLevy r c alpha gets a variate from the Levy symmetric stable distribution with scale c and exponent alpha. The algorithm only works for 0 <= alpha <= 2.

getLevySkew :: RNG -> Double -> Double -> Double -> IO Double

getLevySkew r c alpha beta gets a variate from the Levy skew stable distribution with scale c, exponent alpha, and skewness parameter beta. The skewness parameter must lie in the range [-1,1]. The algorithm only works for 0 <= alpha <= 2.

The Poisson Distribution

poissonPdf :: Int -> Double -> Double

poissonPdf k mu evaluates the probability density p(k) at k for a Poisson distribution with mean mu.

poissonP :: Int -> Double -> Double

poissonP k mu evaluates the cumulative distribution function P(k) at k for a Poisson distribution with mean mu.

poissonQ :: Int -> Double -> Double

poissonQ k mu evaluates the cumulative distribution function Q(k) at k for a Poisson distribution with mean mu.

getPoisson :: RNG -> Double -> IO Int

getPoisson r mu gets a poisson random variable with mean mu.