{- - ``Data/Random/Distribution'' -} {-# LANGUAGE MultiParamTypeClasses, FlexibleContexts #-} module Data.Random.Distribution where import Data.Random.Lift import Data.Random.RVar -- |A definition of a random variable's distribution. From the distribution -- an 'RVar' can be created, or the distribution can be directly sampled using -- 'sampleFrom' or 'sample'. class Distribution d t where -- |Return a random variable with this distribution. rvar :: d t -> RVar t class Distribution d t => CDF d t where -- |Return the cumulative distribution function of this distribution. -- That is, a function taking @x :: t@ to the probability that the next -- sample will return a value less than or equal to x, according to some -- order or partial order (not necessarily an obvious one). -- -- In the case where 't' is an instance of Ord, 'cdf' should correspond -- to the CDF with respect to that order. -- -- In other cases, 'cdf' is only required to satisfy the following law: -- @fmap (cdf d) (rvar d)@ -- must be uniformly distributed over (0,1). Inclusion of either endpoint is optional, -- though the preferred range is (0,1]. -- -- Thus, 'cdf' for a product type should not be a joint CDF as commonly -- defined, as that definition violates both conditions. -- Instead, it should be a univariate CDF over the product type. That is, -- it should represent the CDF with respect to the lexicographic order -- of the tuple. cdf :: d t -> t -> Double -- |Return a random variable with the given distribution, pre-lifted to an arbitrary 'RVarT'. -- Any arbitrary 'RVar' can also be converted to an 'RVarT m' for an arbitrary 'm', using -- either 'lift' or 'sample'. rvarT :: Distribution d t => d t -> RVarT n t rvarT d = lift (rvar d)