```{-# LANGUAGE DeriveDataTypeable, DeriveGeneric #-}
-- |
-- Module    : Statistics.Distribution.Hypergeometric
-- Copyright : (c) 2009 Bryan O'Sullivan
--
-- Maintainer  : bos@serpentine.com
-- Stability   : experimental
-- Portability : portable
--
-- The Hypergeometric distribution.  This is the discrete probability
-- distribution that measures the probability of /k/ successes in /l/
-- trials, without replacement, from a finite population.
--
-- The parameters of the distribution describe /k/ elements chosen
-- from a population of /l/, with /m/ elements of one type, and
-- /l/-/m/ of the other (all are positive integers).

module Statistics.Distribution.Hypergeometric
(
HypergeometricDistribution
-- * Constructors
, hypergeometric
-- ** Accessors
, hdM
, hdL
, hdK
) where

import Data.Binary (Binary)
import Data.Data (Data, Typeable)
import GHC.Generics (Generic)
import Numeric.MathFunctions.Constants (m_epsilon)
import Numeric.SpecFunctions (choose)
import qualified Statistics.Distribution as D
import Data.Binary (put, get)
import Control.Applicative ((<\$>), (<*>))

data HypergeometricDistribution = HD {
hdM :: {-# UNPACK #-} !Int
, hdL :: {-# UNPACK #-} !Int
, hdK :: {-# UNPACK #-} !Int
} deriving (Eq, Read, Show, Typeable, Data, Generic)

instance Binary HypergeometricDistribution where
get = HD <\$> get <*> get <*> get
put (HD x y z) = put x >> put y >> put z

instance D.Distribution HypergeometricDistribution where
cumulative = cumulative

instance D.DiscreteDistr HypergeometricDistribution where
probability = probability

instance D.Mean HypergeometricDistribution where
mean = mean

instance D.Variance HypergeometricDistribution where
variance = variance

instance D.MaybeMean HypergeometricDistribution where
maybeMean = Just . D.mean

instance D.MaybeVariance HypergeometricDistribution where
maybeStdDev   = Just . D.stdDev
maybeVariance = Just . D.variance

instance D.Entropy HypergeometricDistribution where
entropy = directEntropy

instance D.MaybeEntropy HypergeometricDistribution where
maybeEntropy = Just . D.entropy

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'
{-# INLINE variance #-}

mean :: HypergeometricDistribution -> Double
mean (HD m l k) = fromIntegral k * fromIntegral m / fromIntegral l
{-# INLINE mean #-}

directEntropy :: HypergeometricDistribution -> Double
directEntropy d@(HD m _ _) =
negate . sum \$
takeWhile (< negate m_epsilon) \$
dropWhile (not . (< negate m_epsilon)) \$
[ let x = probability d n in x * log x | n <- [0..m]]

hypergeometric :: Int               -- ^ /m/
-> Int               -- ^ /l/
-> Int               -- ^ /k/
-> HypergeometricDistribution
hypergeometric m l k
| not (l > 0)            = error \$ msg ++ "l must be positive"
| not (m >= 0 && m <= l) = error \$ msg ++ "m must lie in [0,l] range"
| not (k > 0 && k <= l)  = error \$ msg ++ "k must lie in (0,l] range"
| otherwise = HD m l k
where
msg = "Statistics.Distribution.Hypergeometric.hypergeometric: "
{-# INLINE hypergeometric #-}

-- Naive implementation
probability :: HypergeometricDistribution -> Int -> Double
probability (HD mi li ki) n
| n < max 0 (mi+ki-li) || n > min mi ki = 0
| otherwise =
choose mi n * choose (li - mi) (ki - n) / choose li ki
{-# INLINE probability #-}

cumulative :: HypergeometricDistribution -> Double -> Double
cumulative d@(HD mi li ki) x
| isNaN x      = error "Statistics.Distribution.Hypergeometric.cumulative: NaN argument"
| isInfinite x = if x > 0 then 1 else 0
| n <  minN    = 0
| n >= maxN    = 1
| otherwise    = D.sumProbabilities d minN n
where
n    = floor x
minN = max 0 (mi+ki-li)
maxN = min mi ki
```