module Statistics.Distribution.CauchyLorentz (
CauchyDistribution
, cauchyDistribMedian
, cauchyDistribScale
, cauchyDistribution
, standardCauchy
) where
import Data.Binary (Binary)
import Data.Data (Data, Typeable)
import GHC.Generics (Generic)
import qualified Statistics.Distribution as D
import Data.Binary (put, get)
import Control.Applicative ((<$>), (<*>))
data CauchyDistribution = CD {
cauchyDistribMedian :: !Double
, cauchyDistribScale :: !Double
}
deriving (Eq, Show, Read, Typeable, Data, Generic)
instance Binary CauchyDistribution where
put (CD x y) = put x >> put y
get = CD <$> get <*> get
cauchyDistribution :: Double
-> Double
-> CauchyDistribution
cauchyDistribution m s
| s > 0 = CD m s
| otherwise =
error $ "Statistics.Distribution.CauchyLorentz.cauchyDistribution: FWHM must be positive. Got " ++ show s
standardCauchy :: CauchyDistribution
standardCauchy = CD 0 1
instance D.Distribution CauchyDistribution where
cumulative (CD m s) x = 0.5 + atan( (x m) / s ) / pi
instance D.ContDistr CauchyDistribution where
density (CD m s) x = (1 / pi) / (s * (1 + y*y))
where y = (x m) / s
quantile (CD m s) p
| p > 0 && p < 1 = m + s * tan( pi * (p 0.5) )
| p == 0 = 1 / 0
| p == 1 = 1 / 0
| otherwise =
error $ "Statistics.Distribution.CauchyLorentz..quantile: p must be in [0,1] range. Got: "++show p
instance D.ContGen CauchyDistribution where
genContVar = D.genContinous
instance D.Entropy CauchyDistribution where
entropy (CD _ s) = log s + log (4*pi)
instance D.MaybeEntropy CauchyDistribution where
maybeEntropy = Just . D.entropy