{- - ``Data/Random/Distribution/Triangular'' -} {-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FlexibleContexts, UndecidableInstances #-} module Data.Random.Distribution.Triangular where import Data.Random.RVar import Data.Random.Distribution import Data.Random.Distribution.Uniform -- |A description of a triangular distribution - a distribution whose PDF -- is a triangle ramping up from a lower bound to a specified midpoint -- and back down to the upper bound. This is a very simple distribution -- that does not generally occur naturally but is used sometimes as an -- estimate of a true distribution when only the range of the values and -- an approximate mode of the true distribution are known. data Triangular a = Triangular { -- |The lower bound of the triangle in the PDF (the smallest number the distribution can generate) triLower :: a, -- |The midpoint of the triangle (also the mode of the distribution) triMid :: a, -- |The upper bound of the triangle (and the largest number the distribution can generate) triUpper :: a} deriving (Eq, Show) -- |Compute a triangular distribution for a 'Floating' type. floatingTriangular :: (Floating a, Ord a, Distribution StdUniform a) => a -> a -> a -> RVarT m a floatingTriangular a b c | a > b = floatingTriangular b a c | b > c = floatingTriangular a c b | otherwise = do let p = (c-b)/(c-a) u <- stdUniformT let d | u >= p = a | otherwise = c x | u >= p = (u - p) / (1 - p) | otherwise = u / p -- may prefer this: reusing u costs resolution, especially if p or 1-p is small and c-a is large. -- x <- stdUniform return (b - ((1 - sqrt x) * (b-d))) -- |@triangularCDF a b c@ is the CDF of @realFloatTriangular a b c@. triangularCDF :: RealFrac a => a -> a -> a -> a -> Double triangularCDF a b c x | x < a = 0 | x <= b = realToFrac ((x - a)^(2 :: Int) / ((c - a) * (b - a))) | x <= c = realToFrac (1 - (c - x)^(2 :: Int) / ((c - a) * (c - b))) | otherwise = 1 instance (RealFloat a, Ord a, Distribution StdUniform a) => Distribution Triangular a where rvarT (Triangular a b c) = floatingTriangular a b c instance (RealFrac a, Distribution Triangular a) => CDF Triangular a where cdf (Triangular a b c) = triangularCDF a b c