module Statistics.Distribution.Poisson
(
PoissonDistribution
, poisson
, poissonLambda
) 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,logFactorial)
import Numeric.MathFunctions.Constants (m_neg_inf)
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
instance D.DiscreteDistr PoissonDistribution where
probability (PD lambda) x = I.probability lambda (fromIntegral x)
logProbability (PD lambda) i
| i < 0 = m_neg_inf
| otherwise = log lambda * fromIntegral i logFactorial i lambda
instance D.Variance PoissonDistribution where
variance = poissonLambda
instance D.Mean PoissonDistribution where
mean = poissonLambda
instance D.MaybeMean PoissonDistribution where
maybeMean = Just . D.mean
instance D.MaybeVariance PoissonDistribution where
maybeStdDev = Just . D.stdDev
instance D.Entropy PoissonDistribution where
entropy (PD lambda) = I.poissonEntropy lambda
instance D.MaybeEntropy PoissonDistribution where
maybeEntropy = Just . D.entropy
poisson :: Double -> PoissonDistribution
poisson l
| l >= 0 = PD l
| otherwise = error $ "Statistics.Distribution.Poisson.poisson:\
\ lambda must be non-negative. Got " ++ show l