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|
{-# LANGUAGE DeriveDataTypeable #-}
-- |
-- Module : Statistics.Distribution.Poisson
-- Copyright : (c) 2009 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
, fromLambda
-- , fromSample
) where
import Data.Typeable (Typeable)
import qualified Data.Vector.Unboxed as U
import qualified Statistics.Distribution as D
import Statistics.Constants (m_huge)
import Statistics.Math (logGamma)
newtype PoissonDistribution = PD {
pdLambda :: Double
} deriving (Eq, Read, Show, Typeable)
instance D.Distribution PoissonDistribution where
density = density
cumulative = cumulative
quantile = quantile
instance D.Variance PoissonDistribution where
variance = pdLambda
{-# INLINE variance #-}
instance D.Mean PoissonDistribution where
mean = pdLambda
{-# INLINE mean #-}
fromLambda :: Double -> PoissonDistribution
fromLambda = PD
{-# INLINE fromLambda #-}
density :: PoissonDistribution -> Double -> Double
density (PD l) x = exp (x * log l - l - logGamma x)
{-# INLINE density #-}
cumulative :: PoissonDistribution -> Double -> Double
cumulative d = U.sum . U.map (density d . fromIntegral) .
U.enumFromTo (0::Int) . floor
{-# INLINE cumulative #-}
quantile :: PoissonDistribution -> Double -> Double
quantile d p = fromIntegral . r $ D.findRoot d p (pdLambda d) 0 m_huge
where r = round :: Double -> Int
{-# INLINE quantile #-}
|
