module Statistics.Distribution.Hypergeometric
(
HypergeometricDistribution
, hypergeometric
, hdM
, hdL
, hdK
) where
import Control.Exception (assert)
import Data.Typeable (Typeable)
import Statistics.Math (choose)
import qualified Statistics.Distribution as D
data HypergeometricDistribution = HD {
hdM :: !Int
, hdL :: !Int
, hdK :: !Int
} deriving (Eq, Read, Show, Typeable)
instance D.Distribution HypergeometricDistribution where
cumulative d x = D.sumProbabilities d 0 (floor x)
instance D.DiscreteDistr HypergeometricDistribution where
probability = probability
instance D.Variance HypergeometricDistribution where
variance = variance
instance D.Mean HypergeometricDistribution where
mean = mean
variance :: HypergeometricDistribution -> Double
variance (HD m l k) = (k' * ml) * (1 ml) * (l' k') / (l' 1)
where m' = fromIntegral m
l' = fromIntegral l
k' = fromIntegral k
ml = m' / l'
mean :: HypergeometricDistribution -> Double
mean (HD m l k) = fromIntegral k * fromIntegral m / fromIntegral l
hypergeometric :: Int
-> Int
-> Int
-> HypergeometricDistribution
hypergeometric m l k =
assert (m >= 0 && m <= l) .
assert (l > 0) .
assert (k > 0 && k <= l) $
HD m l k
probability :: HypergeometricDistribution -> Int -> Double
probability (HD mi li ki) n
| n < max 0 (mi+kili) || n > min mi ki = 0
| otherwise =
choose mi n * choose (li mi) (ki n) / choose li ki