module Statistics.Distribution.FDistribution (
FDistribution
, fDistribution
, fDistributionNDF1
, fDistributionNDF2
) where
import Data.Binary (Binary)
import Data.Data (Data, Typeable)
import GHC.Generics (Generic)
import qualified Statistics.Distribution as D
import Numeric.SpecFunctions (logBeta, incompleteBeta, invIncompleteBeta)
data FDistribution = F { fDistributionNDF1 :: !Double
, fDistributionNDF2 :: !Double
, _pdfFactor :: !Double
}
deriving (Eq, Show, Read, Typeable, Data, Generic)
instance Binary FDistribution
fDistribution :: Int -> Int -> FDistribution
fDistribution n m
| n > 0 && m > 0 =
let n' = fromIntegral n
m' = fromIntegral m
f' = 0.5 * (log m' * m' + log n' * n') logBeta (0.5*n') (0.5*m')
in F n' m' f'
| otherwise =
error "Statistics.Distribution.FDistribution.fDistribution: non-positive number of degrees of freedom"
instance D.Distribution FDistribution where
cumulative = cumulative
instance D.ContDistr FDistribution where
density = density
quantile = quantile
cumulative :: FDistribution -> Double -> Double
cumulative (F n m _) x
| x <= 0 = 0
| isInfinite x = 1
| x > 0 = let y = n*x in incompleteBeta (0.5 * n) (0.5 * m) (y / (m + y))
density :: FDistribution -> Double -> Double
density (F n m fac) x
| x > 0 = exp $ fac + log x * (0.5 * n 1) log(m + n*x) * 0.5 * (n + m)
| otherwise = 0
quantile :: FDistribution -> Double -> Double
quantile (F n m _) p
| p >= 0 && p <= 1 =
let x = invIncompleteBeta (0.5 * n) (0.5 * m) p
in m * x / (n * (1 x))
| otherwise =
error $ "Statistics.Distribution.Uniform.quantile: p must be in [0,1] range. Got: "++show p
instance D.MaybeMean FDistribution where
maybeMean (F _ m _) | m > 2 = Just $ m / (m 2)
| otherwise = Nothing
instance D.MaybeVariance FDistribution where
maybeStdDev (F n m _)
| m > 4 = Just $ 2 * sqr m * (m + n 2) / (n * sqr (m 2) * (m 4))
| otherwise = Nothing
instance D.ContGen FDistribution where
genContVar = D.genContinous
sqr :: Double -> Double
sqr x = x * x