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|
{-# LANGUAGE OverloadedStrings #-}
{-# 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
, hypergeometricE
-- ** Accessors
, hdM
, hdL
, hdK
) where
import Control.Applicative
import Data.Aeson (FromJSON(..), ToJSON, Value(..), (.:))
import Data.Binary (Binary(..))
import Data.Data (Data, Typeable)
import GHC.Generics (Generic)
import Numeric.MathFunctions.Constants (m_epsilon,m_neg_inf)
import Numeric.SpecFunctions (choose,logChoose)
import qualified Statistics.Distribution as D
import Statistics.Internal
data HypergeometricDistribution = HD {
hdM :: {-# UNPACK #-} !Int
, hdL :: {-# UNPACK #-} !Int
, hdK :: {-# UNPACK #-} !Int
} deriving (Eq, Typeable, Data, Generic)
instance Show HypergeometricDistribution where
showsPrec i (HD m l k) = defaultShow3 "hypergeometric" m l k i
instance Read HypergeometricDistribution where
readPrec = defaultReadPrecM3 "hypergeometric" hypergeometricE
instance ToJSON HypergeometricDistribution
instance FromJSON HypergeometricDistribution where
parseJSON (Object v) = do
m <- v .: "hdM"
l <- v .: "hdL"
k <- v .: "hdK"
maybe (fail $ errMsg m l k) return $ hypergeometricE m l k
parseJSON _ = empty
instance Binary HypergeometricDistribution where
put (HD m l k) = put m >> put l >> put k
get = do
m <- get
l <- get
k <- get
maybe (fail $ errMsg m l k) return $ hypergeometricE m l k
instance D.Distribution HypergeometricDistribution where
cumulative = cumulative
complCumulative = complCumulative
instance D.DiscreteDistr HypergeometricDistribution where
probability = probability
logProbability = logProbability
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
= maybe (error $ errMsg m l k) id $ hypergeometricE m l k
hypergeometricE :: Int -- ^ /m/
-> Int -- ^ /l/
-> Int -- ^ /k/
-> Maybe HypergeometricDistribution
hypergeometricE m l k
| not (l > 0) = Nothing
| not (m >= 0 && m <= l) = Nothing
| not (k > 0 && k <= l) = Nothing
| otherwise = Just (HD m l k)
errMsg :: Int -> Int -> Int -> String
errMsg m l k
= "Statistics.Distribution.Hypergeometric.hypergeometric:"
++ " m=" ++ show m
++ " l=" ++ show l
++ " k=" ++ show k
++ " should hold: l>0 & m in [0,l] & k in (0,l]"
-- Naive implementation
probability :: HypergeometricDistribution -> Int -> Double
probability (HD mi li ki) n
| n < max 0 (mi+ki-li) || n > min mi ki = 0
-- No overflow
| li < 1000 = choose mi n * choose (li - mi) (ki - n)
/ choose li ki
| otherwise = exp $ logChoose mi n
+ logChoose (li - mi) (ki - n)
- logChoose li ki
logProbability :: HypergeometricDistribution -> Int -> Double
logProbability (HD mi li ki) n
| n < max 0 (mi+ki-li) || n > min mi ki = m_neg_inf
| otherwise = logChoose mi n
+ logChoose (li - mi) (ki - n)
- logChoose 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
complCumulative :: HypergeometricDistribution -> Double -> Double
complCumulative d@(HD mi li ki) x
| isNaN x = error "Statistics.Distribution.Hypergeometric.complCumulative: NaN argument"
| isInfinite x = if x > 0 then 0 else 1
| n < minN = 1
| n >= maxN = 0
| otherwise = D.sumProbabilities d (n + 1) maxN
where
n = floor x
minN = max 0 (mi+ki-li)
maxN = min mi ki
|
