{-# LANGUAGE DeriveDataTypeable, DeriveGeneric #-} -- | -- Module : Statistics.Distribution.Poisson -- Copyright : (c) 2009, 2011 Bryan O'Sullivan -- License : BSD3 -- -- Maintainer : bos@serpentine.com -- Stability : experimental -- Portability : portable -- -- The Poisson distribution. This is the discrete probability -- distribution of a number of events occurring in a fixed interval if -- these events occur with a known average rate, and occur -- independently from each other within that interval. module Statistics.Distribution.Poisson ( PoissonDistribution -- * Constructors , poisson -- * Accessors , poissonLambda -- * References -- \$references ) where import Data.Binary (Binary) import Data.Data (Data, Typeable) import GHC.Generics (Generic) import qualified Statistics.Distribution as D import qualified Statistics.Distribution.Poisson.Internal as I import Numeric.SpecFunctions (incompleteGamma) newtype PoissonDistribution = PD { poissonLambda :: Double } deriving (Eq, Read, Show, Typeable, Data, Generic) instance Binary PoissonDistribution instance D.Distribution PoissonDistribution where cumulative (PD lambda) x | x < 0 = 0 | isInfinite x = 1 | isNaN x = error "Statistics.Distribution.Poisson.cumulative: NaN input" | otherwise = 1 - incompleteGamma (fromIntegral (floor x + 1 :: Int)) lambda {-# INLINE cumulative #-} instance D.DiscreteDistr PoissonDistribution where probability (PD lambda) x = I.probability lambda (fromIntegral x) {-# INLINE probability #-} instance D.Variance PoissonDistribution where variance = poissonLambda {-# INLINE variance #-} instance D.Mean PoissonDistribution where mean = poissonLambda {-# INLINE mean #-} instance D.MaybeMean PoissonDistribution where maybeMean = Just . D.mean instance D.MaybeVariance PoissonDistribution where maybeStdDev = Just . D.stdDev -- | Create Poisson distribution. poisson :: Double -> PoissonDistribution poisson l | l >= 0 = PD l | otherwise = error \$ "Statistics.Distribution.Poisson.poisson:\ \ lambda must be non-negative. Got " ++ show l {-# INLINE poisson #-} -- \$references -- -- * Loader, C. (2000) Fast and Accurate Computation of Binomial -- Probabilities.