{-# LANGUAGE DeriveDataTypeable, DeriveGeneric #-} -- | -- Module : Statistics.Distribution.Hypergeometric -- Copyright : (c) 2009 Bryan O'Sullivan -- License : BSD3 -- -- 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.Aeson (FromJSON, ToJSON) 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 FromJSON HypergeometricDistribution instance ToJSON HypergeometricDistribution 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' mean :: HypergeometricDistribution -> Double mean (HD m l k) = fromIntegral k * fromIntegral m / fromIntegral l 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: " -- 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 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