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{-# LANGUAGE DeriveDataTypeable #-}
-- |
-- Module : Statistics.Distribution.Uniform
-- Copyright : (c) 2011 Aleksey Khudyakov
-- License : BSD3
--
-- Maintainer : bos@serpentine.com
-- Stability : experimental
-- Portability : portable
--
-- Variate distributed uniformly in the interval.
module Statistics.Distribution.Uniform (
UniformDistribution
, uniformDistr
) where
import Data.Typeable (Typeable)
import qualified Statistics.Distribution as D
import qualified System.Random.MWC as MWC
-- | Uniform distribution
data UniformDistribution = UniformDistribution {-# UNPACK #-} !Double {-# UNPACK #-} !Double
deriving (Eq,Show,Read,Typeable)
-- | Create uniform distribution.
uniformDistr :: Double -> Double -> UniformDistribution
uniformDistr a b
| b < a = uniformDistr b a
| a < b = UniformDistribution a b
| otherwise = error "Statistics.Distribution.Uniform.uniform: wrong parameters"
-- NOTE: failure is in default branch to guard againist NaNs.
instance D.Distribution UniformDistribution where
cumulative (UniformDistribution a b) x
| x < a = 0
| x > b = 1
| otherwise = (x - a) / (b - a)
instance D.ContDistr UniformDistribution where
density (UniformDistribution a b) x
| x < a = 0
| x > b = 0
| otherwise = 1 / (b - a)
quantile (UniformDistribution a b) p
| p >= 0 && p <= 1 = a + (b - a) * p
| otherwise =
error $ "Statistics.Distribution.Uniform.quantile: p must be in [0,1] range. Got: "++show p
instance D.Mean UniformDistribution where
mean (UniformDistribution a b) = 0.5 * (a + b)
instance D.Variance UniformDistribution where
-- NOTE: 1/sqrt 12 is not constant folded (#4101) so it's written as
-- numerical constant. (Also FIXME!)
stdDev (UniformDistribution a b) = 0.2886751345948129 * (b - a)
variance (UniformDistribution a b) = d * d / 12 where d = b - a
instance D.MaybeMean UniformDistribution where
maybeMean = Just . D.mean
instance D.MaybeVariance UniformDistribution where
maybeStdDev = Just . D.stdDev
instance D.ContGen UniformDistribution where
genContVar (UniformDistribution a b) gen = MWC.uniformR (a,b) gen
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