{-# 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).moduleStatistics.Distribution.Hypergeometric(HypergeometricDistribution -- * Constructors,hypergeometric ,hypergeometricE -- ** Accessors,hdM ,hdL ,hdK )whereimportControl.ApplicativeimportData.Aeson(FromJSON(..),ToJSON,Value(..),(.:))importData.Binary(Binary(..))importData.Data(Data,Typeable)importGHC.Generics(Generic)importNumeric.MathFunctions.Constants(m_epsilon,m_neg_inf)importNumeric.SpecFunctions(choose,logChoose)importqualifiedStatistics.Distribution asDimportStatistics.Internal dataHypergeometricDistribution =HD {HypergeometricDistribution -> Int
hdM ::{-# UNPACK#-}!Int,HypergeometricDistribution -> Int
hdL ::{-# UNPACK#-}!Int,HypergeometricDistribution -> Int
hdK ::{-# UNPACK#-}!Int}deriving(HypergeometricDistribution -> HypergeometricDistribution -> Bool
(HypergeometricDistribution -> HypergeometricDistribution -> Bool)
-> (HypergeometricDistribution
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-> Eq HypergeometricDistribution
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
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/= :: HypergeometricDistribution -> HypergeometricDistribution -> Bool
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-> Data HypergeometricDistribution
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HypergeometricDistribution -> DataType
(forall b. Data b => b -> b)
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forall (c :: * -> *).
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$cgmapT :: (forall b. Data b => b -> b)
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gmapT :: (forall b. Data b => b -> b)
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gmapQl :: forall r r'.
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gmapQr :: forall r r'.
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gmapQ :: forall u.
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gmapQi :: forall u.
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$cgmapM :: forall (m :: * -> *).
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gmapM :: forall (m :: * -> *).
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gmapMp :: forall (m :: * -> *).
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-> HypergeometricDistribution -> m HypergeometricDistribution
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gmapMo :: forall (m :: * -> *).
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Data,(forall x.
 HypergeometricDistribution -> Rep HypergeometricDistribution x)
-> (forall x.
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-> Generic HypergeometricDistribution
forall x.
Rep HypergeometricDistribution x -> HypergeometricDistribution
forall x.
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from :: forall x.
HypergeometricDistribution -> Rep HypergeometricDistribution x
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to :: forall x.
Rep HypergeometricDistribution x -> HypergeometricDistribution
Generic)instanceShowHypergeometricDistribution whereshowsPrec :: Int -> HypergeometricDistribution -> ShowS
showsPrec Int
i (HD Int
m Int
l Int
k )=[Char] -> Int -> Int -> Int -> Int -> ShowS
forall a b c.
(Show a, Show b, Show c) =>
[Char] -> a -> b -> c -> Int -> ShowS
defaultShow3 [Char]
"hypergeometric"Int
m Int
l Int
k Int
i instanceReadHypergeometricDistribution wherereadPrec :: ReadPrec HypergeometricDistribution
readPrec =[Char]
-> (Int -> Int -> Int -> Maybe HypergeometricDistribution)
-> ReadPrec HypergeometricDistribution
forall a b c r.
(Read a, Read b, Read c) =>
[Char] -> (a -> b -> c -> Maybe r) -> ReadPrec r
defaultReadPrecM3 [Char]
"hypergeometric"Int -> Int -> Int -> Maybe HypergeometricDistribution
hypergeometricE instanceToJSONHypergeometricDistribution instanceFromJSONHypergeometricDistribution whereparseJSON :: Value -> Parser HypergeometricDistribution
parseJSON (ObjectObject
v )=doInt
m <-Object
v Object -> Key -> Parser Int
forall a. FromJSON a => Object -> Key -> Parser a
.:Key
"hdM"Int
l <-Object
v Object -> Key -> Parser Int
forall a. FromJSON a => Object -> Key -> Parser a
.:Key
"hdL"Int
k <-Object
v Object -> Key -> Parser Int
forall a. FromJSON a => Object -> Key -> Parser a
.:Key
"hdK"Parser HypergeometricDistribution
-> (HypergeometricDistribution
 -> Parser HypergeometricDistribution)
-> Maybe HypergeometricDistribution
-> Parser HypergeometricDistribution
forall b a. b -> (a -> b) -> Maybe a -> b
maybe([Char] -> Parser HypergeometricDistribution
forall a. [Char] -> Parser a
forall (m :: * -> *) a. MonadFail m => [Char] -> m a
fail([Char] -> Parser HypergeometricDistribution)
-> [Char] -> Parser HypergeometricDistribution
forall a b. (a -> b) -> a -> b
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errMsg Int
m Int
l Int
k )HypergeometricDistribution -> Parser HypergeometricDistribution
forall a. a -> Parser a
forall (m :: * -> *) a. Monad m => a -> m a
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 -> Parser HypergeometricDistribution)
-> Maybe HypergeometricDistribution
-> Parser HypergeometricDistribution
forall a b. (a -> b) -> a -> b
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hypergeometricE Int
m Int
l Int
k parseJSONValue
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forall a. Parser a
forall (f :: * -> *) a. Alternative f => f a
emptyinstanceBinaryHypergeometricDistribution whereput :: HypergeometricDistribution -> Put
put (HD Int
m Int
l Int
k )=Int -> Put
forall t. Binary t => t -> Put
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m Put -> Put -> Put
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putInt
k get :: Get HypergeometricDistribution
get =doInt
m <-Get Int
forall t. Binary t => Get t
getInt
l <-Get Int
forall t. Binary t => Get t
getInt
k <-Get Int
forall t. Binary t => Get t
getGet HypergeometricDistribution
-> (HypergeometricDistribution -> Get HypergeometricDistribution)
-> Maybe HypergeometricDistribution
-> Get HypergeometricDistribution
forall b a. b -> (a -> b) -> Maybe a -> b
maybe([Char] -> Get HypergeometricDistribution
forall a. [Char] -> Get a
forall (m :: * -> *) a. MonadFail m => [Char] -> m a
fail([Char] -> Get HypergeometricDistribution)
-> [Char] -> Get HypergeometricDistribution
forall a b. (a -> b) -> a -> b
$Int -> Int -> Int -> [Char]
errMsg Int
m Int
l Int
k )HypergeometricDistribution -> Get HypergeometricDistribution
forall a. a -> Get a
forall (m :: * -> *) a. Monad m => a -> m a
return(Maybe HypergeometricDistribution
 -> Get HypergeometricDistribution)
-> Maybe HypergeometricDistribution
-> Get HypergeometricDistribution
forall a b. (a -> b) -> a -> b
$Int -> Int -> Int -> Maybe HypergeometricDistribution
hypergeometricE Int
m Int
l Int
k instanceD.Distribution HypergeometricDistribution wherecumulative :: HypergeometricDistribution -> Double -> Double
cumulative =HypergeometricDistribution -> Double -> Double
cumulative complCumulative :: HypergeometricDistribution -> Double -> Double
complCumulative =HypergeometricDistribution -> Double -> Double
complCumulative instanceD.DiscreteDistr HypergeometricDistribution whereprobability :: HypergeometricDistribution -> Int -> Double
probability =HypergeometricDistribution -> Int -> Double
probability logProbability :: HypergeometricDistribution -> Int -> Double
logProbability =HypergeometricDistribution -> Int -> Double
logProbability instanceD.Mean HypergeometricDistribution wheremean :: HypergeometricDistribution -> Double
mean =HypergeometricDistribution -> Double
mean instanceD.Variance HypergeometricDistribution wherevariance :: HypergeometricDistribution -> Double
variance =HypergeometricDistribution -> Double
variance instanceD.MaybeMean HypergeometricDistribution wheremaybeMean :: HypergeometricDistribution -> Maybe Double
maybeMean =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (HypergeometricDistribution -> Double)
-> HypergeometricDistribution
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.HypergeometricDistribution -> Double
forall d. Mean d => d -> Double
D.mean instanceD.MaybeVariance HypergeometricDistribution wheremaybeStdDev :: HypergeometricDistribution -> Maybe Double
maybeStdDev =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (HypergeometricDistribution -> Double)
-> HypergeometricDistribution
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.HypergeometricDistribution -> Double
forall d. Variance d => d -> Double
D.stdDev maybeVariance :: HypergeometricDistribution -> Maybe Double
maybeVariance =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (HypergeometricDistribution -> Double)
-> HypergeometricDistribution
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.HypergeometricDistribution -> Double
forall d. Variance d => d -> Double
D.variance instanceD.Entropy HypergeometricDistribution whereentropy :: HypergeometricDistribution -> Double
entropy =HypergeometricDistribution -> Double
directEntropy instanceD.MaybeEntropy HypergeometricDistribution wheremaybeEntropy :: HypergeometricDistribution -> Maybe Double
maybeEntropy =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (HypergeometricDistribution -> Double)
-> HypergeometricDistribution
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.HypergeometricDistribution -> Double
forall d. Entropy d => d -> Double
D.entropy variance ::HypergeometricDistribution ->Doublevariance :: HypergeometricDistribution -> Double
variance (HD Int
m Int
l Int
k )=(Double
k' Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double
ml )Double -> Double -> Double
forall a. Num a => a -> a -> a
*(Double
1Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
ml )Double -> Double -> Double
forall a. Num a => a -> a -> a
*(Double
l' Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
k' )Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/(Double
l' Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
1)wherem' :: Double
m' =Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
m l' :: Double
l' =Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
l k' :: Double
k' =Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
k ml :: Double
ml =Double
m' Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/Double
l' mean ::HypergeometricDistribution ->Doublemean :: HypergeometricDistribution -> Double
mean (HD Int
m Int
l Int
k )=Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
k Double -> Double -> Double
forall a. Num a => a -> a -> a
*Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
m Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
l directEntropy ::HypergeometricDistribution ->DoubledirectEntropy :: HypergeometricDistribution -> Double
directEntropy d :: HypergeometricDistribution
d @(HD Int
m Int
_Int
_)=Double -> Double
forall a. Num a => a -> a
negate(Double -> Double) -> ([Double] -> Double) -> [Double] -> Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.[Double] -> Double
forall a. Num a => [a] -> a
forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
sum([Double] -> Double) -> [Double] -> Double
forall a b. (a -> b) -> a -> b
$(Double -> Bool) -> [Double] -> [Double]
forall a. (a -> Bool) -> [a] -> [a]
takeWhile(Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
<Double -> Double
forall a. Num a => a -> a
negateDouble
m_epsilon)([Double] -> [Double]) -> [Double] -> [Double]
forall a b. (a -> b) -> a -> b
$(Double -> Bool) -> [Double] -> [Double]
forall a. (a -> Bool) -> [a] -> [a]
dropWhile(Bool -> Bool
not(Bool -> Bool) -> (Double -> Bool) -> Double -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
<Double -> Double
forall a. Num a => a -> a
negateDouble
m_epsilon))[letx :: Double
x =HypergeometricDistribution -> Int -> Double
probability HypergeometricDistribution
d Int
n inDouble
x Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double -> Double
forall a. Floating a => a -> a
logDouble
x |Int
n <-[Int
0..Int
m ]]hypergeometric ::Int-- ^ /m/->Int-- ^ /l/->Int-- ^ /k/->HypergeometricDistribution hypergeometric :: Int -> Int -> Int -> HypergeometricDistribution
hypergeometric Int
m Int
l Int
k =HypergeometricDistribution
-> (HypergeometricDistribution -> HypergeometricDistribution)
-> Maybe HypergeometricDistribution
-> HypergeometricDistribution
forall b a. b -> (a -> b) -> Maybe a -> b
maybe([Char] -> HypergeometricDistribution
forall a. HasCallStack => [Char] -> a
error([Char] -> HypergeometricDistribution)
-> [Char] -> HypergeometricDistribution
forall a b. (a -> b) -> a -> b
$Int -> Int -> Int -> [Char]
errMsg Int
m Int
l Int
k )HypergeometricDistribution -> HypergeometricDistribution
forall a. a -> a
id(Maybe HypergeometricDistribution -> HypergeometricDistribution)
-> Maybe HypergeometricDistribution -> HypergeometricDistribution
forall a b. (a -> b) -> a -> b
$Int -> Int -> Int -> Maybe HypergeometricDistribution
hypergeometricE Int
m Int
l Int
k hypergeometricE ::Int-- ^ /m/->Int-- ^ /l/->Int-- ^ /k/->MaybeHypergeometricDistribution hypergeometricE :: Int -> Int -> Int -> Maybe HypergeometricDistribution
hypergeometricE Int
m Int
l Int
k |Bool -> Bool
not(Int
l Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>Int
0)=Maybe HypergeometricDistribution
forall a. Maybe a
Nothing|Bool -> Bool
not(Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>=Int
0Bool -> Bool -> Bool
&&Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<=Int
l )=Maybe HypergeometricDistribution
forall a. Maybe a
Nothing|Bool -> Bool
not(Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>Int
0Bool -> Bool -> Bool
&&Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<=Int
l )=Maybe HypergeometricDistribution
forall a. Maybe a
Nothing|Bool
otherwise=HypergeometricDistribution -> Maybe HypergeometricDistribution
forall a. a -> Maybe a
Just(Int -> Int -> Int -> HypergeometricDistribution
HD Int
m Int
l Int
k )errMsg ::Int->Int->Int->StringerrMsg :: Int -> Int -> Int -> [Char]
errMsg Int
m Int
l Int
k =[Char]
"Statistics.Distribution.Hypergeometric.hypergeometric:"[Char] -> ShowS
forall a. [a] -> [a] -> [a]
++[Char]
" m="[Char] -> ShowS
forall a. [a] -> [a] -> [a]
++Int -> [Char]
forall a. Show a => a -> [Char]
showInt
m [Char] -> ShowS
forall a. [a] -> [a] -> [a]
++[Char]
" l="[Char] -> ShowS
forall a. [a] -> [a] -> [a]
++Int -> [Char]
forall a. Show a => a -> [Char]
showInt
l [Char] -> ShowS
forall a. [a] -> [a] -> [a]
++[Char]
" k="[Char] -> ShowS
forall a. [a] -> [a] -> [a]
++Int -> [Char]
forall a. Show a => a -> [Char]
showInt
k [Char] -> ShowS
forall a. [a] -> [a] -> [a]
++[Char]
" should hold: l>0 & m in [0,l] & k in (0,l]"-- Naive implementationprobability ::HypergeometricDistribution ->Int->Doubleprobability :: HypergeometricDistribution -> Int -> Double
probability (HD Int
mi Int
li Int
ki )Int
n |Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int -> Int -> Int
forall a. Ord a => a -> a -> a
maxInt
0(Int
mi Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
ki Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
li )Bool -> Bool -> Bool
||Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>Int -> Int -> Int
forall a. Ord a => a -> a -> a
minInt
mi Int
ki =Double
0-- No overflow|Int
li Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int
1000=Int -> Int -> Double
chooseInt
mi Int
n Double -> Double -> Double
forall a. Num a => a -> a -> a
*Int -> Int -> Double
choose(Int
li Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
mi )(Int
ki Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
n )Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/Int -> Int -> Double
chooseInt
li Int
ki |Bool
otherwise=Double -> Double
forall a. Floating a => a -> a
exp(Double -> Double) -> Double -> Double
forall a b. (a -> b) -> a -> b
$Int -> Int -> Double
logChooseInt
mi Int
n Double -> Double -> Double
forall a. Num a => a -> a -> a
+Int -> Int -> Double
logChoose(Int
li Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
mi )(Int
ki Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
n )Double -> Double -> Double
forall a. Num a => a -> a -> a
-Int -> Int -> Double
logChooseInt
li Int
ki logProbability ::HypergeometricDistribution ->Int->DoublelogProbability :: HypergeometricDistribution -> Int -> Double
logProbability (HD Int
mi Int
li Int
ki )Int
n |Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int -> Int -> Int
forall a. Ord a => a -> a -> a
maxInt
0(Int
mi Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
ki Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
li )Bool -> Bool -> Bool
||Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>Int -> Int -> Int
forall a. Ord a => a -> a -> a
minInt
mi Int
ki =Double
m_neg_inf|Bool
otherwise=Int -> Int -> Double
logChooseInt
mi Int
n Double -> Double -> Double
forall a. Num a => a -> a -> a
+Int -> Int -> Double
logChoose(Int
li Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
mi )(Int
ki Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
n )Double -> Double -> Double
forall a. Num a => a -> a -> a
-Int -> Int -> Double
logChooseInt
li Int
ki cumulative ::HypergeometricDistribution ->Double->Doublecumulative :: HypergeometricDistribution -> Double -> Double
cumulative d :: HypergeometricDistribution
d @(HD Int
mi Int
li Int
ki )Double
x |Double -> Bool
forall a. RealFloat a => a -> Bool
isNaNDouble
x =[Char] -> Double
forall a. HasCallStack => [Char] -> a
error[Char]
"Statistics.Distribution.Hypergeometric.cumulative: NaN argument"|Double -> Bool
forall a. RealFloat a => a -> Bool
isInfiniteDouble
x =ifDouble
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
>Double
0thenDouble
1elseDouble
0|Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int
minN =Double
0|Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>=Int
maxN =Double
1|Bool
otherwise=HypergeometricDistribution -> Int -> Int -> Double
forall d. DiscreteDistr d => d -> Int -> Int -> Double
D.sumProbabilities HypergeometricDistribution
d Int
minN Int
n wheren :: Int
n =Double -> Int
forall b. Integral b => Double -> b
forall a b. (RealFrac a, Integral b) => a -> b
floorDouble
x minN :: Int
minN =Int -> Int -> Int
forall a. Ord a => a -> a -> a
maxInt
0(Int
mi Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
ki Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
li )maxN :: Int
maxN =Int -> Int -> Int
forall a. Ord a => a -> a -> a
minInt
mi Int
ki complCumulative ::HypergeometricDistribution ->Double->DoublecomplCumulative :: HypergeometricDistribution -> Double -> Double
complCumulative d :: HypergeometricDistribution
d @(HD Int
mi Int
li Int
ki )Double
x |Double -> Bool
forall a. RealFloat a => a -> Bool
isNaNDouble
x =[Char] -> Double
forall a. HasCallStack => [Char] -> a
error[Char]
"Statistics.Distribution.Hypergeometric.complCumulative: NaN argument"|Double -> Bool
forall a. RealFloat a => a -> Bool
isInfiniteDouble
x =ifDouble
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
>Double
0thenDouble
0elseDouble
1|Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int
minN =Double
1|Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>=Int
maxN =Double
0|Bool
otherwise=HypergeometricDistribution -> Int -> Int -> Double
forall d. DiscreteDistr d => d -> Int -> Int -> Double
D.sumProbabilities HypergeometricDistribution
d (Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)Int
maxN wheren :: Int
n =Double -> Int
forall b. Integral b => Double -> b
forall a b. (RealFrac a, Integral b) => a -> b
floorDouble
x minN :: Int
minN =Int -> Int -> Int
forall a. Ord a => a -> a -> a
maxInt
0(Int
mi Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
ki Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
li )maxN :: Int
maxN =Int -> Int -> Int
forall a. Ord a => a -> a -> a
minInt
mi Int
ki