Copyright	(c) 2012 Bryan O'Sullivan
License	BSD3
Maintainer	bos@serpentine.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

System.Random.MWC.Distributions

Contents

Variates: non-uniformly distributed values
Permutations
References

Description

Pseudo-random number generation for non-uniform distributions.

Synopsis

normal :: StatefulGen g m => Double -> Double -> g -> m Double
standard :: StatefulGen g m => g -> m Double
exponential :: StatefulGen g m => Double -> g -> m Double
truncatedExp :: StatefulGen g m => Double -> (Double, Double) -> g -> m Double
gamma :: StatefulGen g m => Double -> Double -> g -> m Double
chiSquare :: StatefulGen g m => Int -> g -> m Double
beta :: StatefulGen g m => Double -> Double -> g -> m Double
categorical :: (StatefulGen g m, Vector v Double) => v Double -> g -> m Int
logCategorical :: (StatefulGen g m, Vector v Double) => v Double -> g -> m Int
geometric0 :: StatefulGen g m => Double -> g -> m Int
geometric1 :: StatefulGen g m => Double -> g -> m Int
bernoulli :: StatefulGen g m => Double -> g -> m Bool
binomial :: forall g m. StatefulGen g m => Int -> Double -> g -> m Int
dirichlet :: (StatefulGen g m, Traversable t) => t Double -> g -> m (t Double)
uniformPermutation :: forall g m v. (StatefulGen g m, PrimMonad m, Vector v Int) => Int -> g -> m (v Int)
uniformShuffle :: (StatefulGen g m, PrimMonad m, Vector v a) => v a -> g -> m (v a)
uniformShuffleM :: (StatefulGen g m, PrimMonad m, MVector v a) => v (PrimState m) a -> g -> m ()

Variates: non-uniformly distributed values

Continuous distributions

normal Source #

Arguments

:: StatefulGen g m
=> Double	Mean
-> Double	Standard deviation
-> g
-> m Double

Generate a normally distributed random variate with given mean and standard deviation.

standard :: StatefulGen g m => g -> m Double Source #

Generate a normally distributed random variate with zero mean and unit variance.

The implementation uses Doornik's modified ziggurat algorithm. Compared to the ziggurat algorithm usually used, this is slower, but generates more independent variates that pass stringent tests of randomness.

exponential Source #

Arguments

:: StatefulGen g m
=> Double	Scale parameter
-> g	Generator
-> m Double

Generate an exponentially distributed random variate.

truncatedExp Source #

Arguments

:: StatefulGen g m
=> Double	Scale parameter
-> (Double, Double)	Range to which distribution is truncated. Values may be negative.
-> g	Generator.
-> m Double

Generate truncated exponentially distributed random variate.

gamma Source #

Arguments

:: StatefulGen g m
=> Double	Shape parameter
-> Double	Scale parameter
-> g	Generator
-> m Double

Random variate generator for gamma distribution.

chiSquare Source #

Arguments

:: StatefulGen g m
=> Int	Number of degrees of freedom
-> g	Generator
-> m Double

Random variate generator for the chi square distribution.

beta Source #

Arguments

:: StatefulGen g m
=> Double	alpha (>0)
-> Double	beta (>0)
-> g	Generator
-> m Double

Random variate generator for Beta distribution

Discrete distribution

categorical Source #

Arguments

:: (StatefulGen g m, Vector v Double)
=> v Double	List of weights [>0]
-> g	Generator
-> m Int

Random variate generator for categorical distribution.

Note that if you need to generate a lot of variates functions System.Random.MWC.CondensedTable will offer better performance. If only few is needed this function will faster since it avoids costs of setting up table.

logCategorical Source #

Arguments

:: (StatefulGen g m, Vector v Double)
=> v Double	List of logarithms of weights
-> g	Generator
-> m Int

Random variate generator for categorical distribution where the weights are in the log domain. It's implemented in terms of categorical.

geometric0 Source #

Arguments

:: StatefulGen g m
=> Double	p success probability lies in (0,1]
-> g	Generator
-> m Int

Random variate generator for the geometric distribution, computing the number of failures before success. Distribution's support is [0..].

geometric1 Source #

Arguments

:: StatefulGen g m
=> Double	p success probability lies in (0,1]
-> g	Generator
-> m Int

Random variate generator for geometric distribution for number of trials. Distribution's support is [1..] (i.e. just geometric0 shifted by 1).

bernoulli Source #

Arguments

:: StatefulGen g m
=> Double	Probability of success (returning True)
-> g	Generator
-> m Bool

Random variate generator for Bernoulli distribution

binomial Source #

Arguments

:: forall g m. StatefulGen g m
=> Int	Number of trials, must be positive.
-> Double	Probability of success \(p \in [0,1]\)
-> g	Generator
-> m Int

Random variate generator for Binomial distribution. Will throw exception when parameters are out range.

The probability of getting exactly k successes in n trials is given by the probability mass function:

\[ f(k;n,p) = \Pr(X = k) = \binom n k p^k(1-p)^{n-k} \]

Multivariate

dirichlet Source #

Arguments

:: (StatefulGen g m, Traversable t)
=> t Double	container of parameters
-> g	Generator
-> m (t Double)

Random variate generator for Dirichlet distribution

Permutations

uniformPermutation :: forall g m v. (StatefulGen g m, PrimMonad m, Vector v Int) => Int -> g -> m (v Int) Source #

Random variate generator for uniformly distributed permutations. It returns random permutation of vector [0 .. n-1].

This is the Fisher-Yates shuffle

uniformShuffle :: (StatefulGen g m, PrimMonad m, Vector v a) => v a -> g -> m (v a) Source #

Random variate generator for a uniformly distributed shuffle (all shuffles are equiprobable) of a vector. It uses Fisher-Yates shuffle algorithm.

uniformShuffleM :: (StatefulGen g m, PrimMonad m, MVector v a) => v (PrimState m) a -> g -> m () Source #

In-place uniformly distributed shuffle (all shuffles are equiprobable)of a vector.

References

Doornik, J.A. (2005) An improved ziggurat method to generate normal random samples. Mimeo, Nuffield College, University of Oxford. http://www.doornik.com/research/ziggurat.pdf
Thomas, D.B.; Leong, P.G.W.; Luk, W.; Villasenor, J.D. (2007). Gaussian random number generators. ACM Computing Surveys 39(4). http://www.cse.cuhk.edu.hk/~phwl/mt/public/archives/papers/grng_acmcs07.pdf
Kachitvichyanukul, V. and Schmeiser, B. W. Binomial Random Variate Generation. Communications of the ACM, 31, 2 (February, 1988) 216. https://dl.acm.org/doi/pdf/10.1145/42372.42381 Here's an example of how the algorithm's sampling regions look