module Statistics.Distribution.ChiSquared (
ChiSquared
, chiSquared
, chiSquaredNDF
) where
import Data.Typeable (Typeable)
import Statistics.Math (incompleteGamma,invIncompleteGamma,logGamma)
import qualified Statistics.Distribution as D
newtype ChiSquared = ChiSquared Int
deriving (Show,Typeable)
chiSquaredNDF :: ChiSquared -> Int
chiSquaredNDF (ChiSquared ndf) = ndf
chiSquared :: Int -> ChiSquared
chiSquared n
| n <= 0 = error $
"Statistics.Distribution.ChiSquared.chiSquared: N.D.F. must be positive. Got " ++ show n
| otherwise = ChiSquared n
instance D.Distribution ChiSquared where
cumulative = cumulative
instance D.ContDistr ChiSquared where
density = density
quantile = quantile
instance D.Mean ChiSquared where
mean (ChiSquared ndf) = fromIntegral ndf
instance D.Variance ChiSquared where
variance (ChiSquared ndf) = fromIntegral (2*ndf)
instance D.MaybeMean ChiSquared where
maybeMean = Just . D.mean
instance D.MaybeVariance ChiSquared where
maybeStdDev = Just . D.stdDev
maybeVariance = Just . D.variance
cumulative :: ChiSquared -> Double -> Double
cumulative chi x
| x <= 0 = 0
| otherwise = incompleteGamma (ndf/2) (x/2)
where
ndf = fromIntegral $ chiSquaredNDF chi
density :: ChiSquared -> Double -> Double
density chi x
| x <= 0 = 0
| otherwise = exp $ log x * (ndf2 1) x2 logGamma ndf2 log 2 * ndf2
where
ndf = fromIntegral $ chiSquaredNDF chi
ndf2 = ndf/2
x2 = x/2
quantile :: ChiSquared -> Double -> Double
quantile (ChiSquared ndf) p
| p == 0 = 0
| p == 1 = 1/0
| p > 0 && p < 1 = 2 * invIncompleteGamma (fromIntegral ndf / 2) p
| otherwise =
error $ "Statistics.Distribution.ChiSquared.quantile: p must be in [0,1] range. Got: "++show p