module Statistics.Distribution.Poisson
(
PoissonDistribution
, fromLambda
) where
import Data.Array.Vector
import Data.Typeable (Typeable)
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
instance D.Mean PoissonDistribution where
mean = pdLambda
fromLambda :: Double -> PoissonDistribution
fromLambda = PD
density :: PoissonDistribution -> Double -> Double
density (PD l) x = exp (x * log l l logGamma x)
cumulative :: PoissonDistribution -> Double -> Double
cumulative d = sumU . mapU (density d . fromIntegral) .
enumFromToU (0::Int) . floor
quantile :: PoissonDistribution -> Double -> Double
quantile d p = fromIntegral . r $ D.findRoot d p (pdLambda d) 0 m_huge
where r = round :: Double -> Int