System.Random.SplitMix.Distributions

Random samplers for few common distributions, with an interface similar to that of mwc-probability.

Usage

Compose your random sampler out of simpler ones thanks to the Applicative and Monad interface, e.g. this is how you would declare and sample a binary mixture of Gaussian random variables:

import Control.Monad (replicateM)
import System.Random.SplitMix.Distributions (Gen, sample, bernoulli, normal)

process :: Gen Double
process = do
  coin <- bernoulli 0.7
  if coin
    then
      normal 0 2
    else
      normal 3 1

dataset :: [Double]
dataset = sample 1234 $ replicateM 20 process

and sample your data in a pure (sample) or monadic (sampleT) setting.

Implementation details

The library is built on top of splitmix, so the caveats on safety and performance that apply there are relevant here as well.

Distributions

Continuous

stdUniform :: Gen Double

Uniform in [0, 1)

uniformR

Arguments

:: Double

low

-> Double

high

-> Gen Double

Uniform between two values

exponential

Arguments

:: Double

rate parameter \( \lambda > 0 \)

-> Gen Double

Exponential distribution

stdNormal :: Gen Double

Standard normal

normal

Arguments

:: Double

mean

-> Double

standard deviation \( \sigma \gt 0 \)

-> Gen Double

Normal distribution

beta

Arguments

:: Double

shape parameter \( \alpha \gt 0 \)

-> Double

shape parameter \( \beta \gt 0 \)

-> Gen Double

Beta distribution, from two standard uniform samples

gamma

Arguments

:: Double

shape parameter \( k \gt 0 \)

-> Double

scale parameter \( \theta \gt 0 \)

-> Gen Double

Gamma distribution, using Ahrens-Dieter accept-reject (algorithm GD):

Ahrens, J. H.; Dieter, U (January 1982). "Generating gamma variates by a modified rejection technique". Communications of the ACM. 25 (1): 47–54

Discrete

bernoulli

Arguments

:: Double

bias parameter \( 0 \lt p \lt 1 \)

-> Gen Bool

Bernoulli trial

PRNG

Pure

type Gen = GenT Identity

Pure random generation

sample

Arguments

:: Word64

random seed

-> Gen a

-> a

Pure evaluation

Monadic

data GenT m a

Random generator

wraps splitmix state-passing inside a StateT monad

useful for embedding random generation inside a larger effect stack

Instances

MonadTrans GenT

Defined in System.Random.SplitMix.Distributions

Methods

lift :: Monad m => m a -> GenT m a

Monad m => MonadState SMGen (GenT m)

Defined in System.Random.SplitMix.Distributions

Methods

get :: GenT m SMGen

put :: SMGen -> GenT m ()

state :: (SMGen -> (a, SMGen)) -> GenT m a

Monad m => Monad (GenT m)

Defined in System.Random.SplitMix.Distributions

Methods

(>>=) :: GenT m a -> (a -> GenT m b) -> GenT m b

(>>) :: GenT m a -> GenT m b -> GenT m b

return :: a -> GenT m a

Functor m => Functor (GenT m)

Defined in System.Random.SplitMix.Distributions

Methods

fmap :: (a -> b) -> GenT m a -> GenT m b

(<$) :: a -> GenT m b -> GenT m a

Monad m => Applicative (GenT m)

Defined in System.Random.SplitMix.Distributions

Methods

pure :: a -> GenT m a

(<*>) :: GenT m (a -> b) -> GenT m a -> GenT m b

liftA2 :: (a -> b -> c) -> GenT m a -> GenT m b -> GenT m c

(*>) :: GenT m a -> GenT m b -> GenT m b

(<*) :: GenT m a -> GenT m b -> GenT m a

MonadIO m => MonadIO (GenT m)

Defined in System.Random.SplitMix.Distributions

Methods

liftIO :: IO a -> GenT m a

sampleT

Arguments

:: Monad m

=> Word64

random seed

-> GenT m a

-> m a

Monadic evaluation

withGen

Arguments

:: Monad m

=> (SMGen -> (a, SMGen))

explicit generator passing (e.g. nextDouble)

-> GenT m a

Wrap a splitmix PRNG function