module Statistics.Distribution.Poisson
(
PoissonDistribution
, poisson
, poissonLambda
) where
import Data.Typeable (Typeable)
import qualified Statistics.Distribution as D
import Statistics.Math (logGamma, factorial)
newtype PoissonDistribution = PD {
poissonLambda :: Double
} deriving (Eq, Read, Show, Typeable)
instance D.Distribution PoissonDistribution where
cumulative d x = D.sumProbabilities d 0 (floor x)
instance D.DiscreteDistr PoissonDistribution where
probability = probability
instance D.Variance PoissonDistribution where
variance = poissonLambda
instance D.Mean PoissonDistribution where
mean = poissonLambda
poisson :: Double -> PoissonDistribution
poisson = PD
probability :: PoissonDistribution -> Int -> Double
probability (PD l) n
| n < 0 = 0
| l < 20 && n <= 100 = exp (l) * l ** x / factorial n
| otherwise = exp (x * log l logGamma (x + 1) l)
where
x = fromIntegral n