{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveGeneric #-}
module ELynx.Distribution.TimeOfOriginNearCritical
( TimeOfOriginNearCriticalDistribution(..)
, cumulative
, density
, quantile
) where
import Data.Data (Data, Typeable)
import GHC.Generics (Generic)
import qualified Statistics.Distribution as D
import ELynx.Distribution.Types
data TimeOfOriginNearCriticalDistribution = TONCD
{ todTN :: Int
, todLa :: Rate
, todMu :: Rate
} deriving (Eq, Typeable, Data, Generic)
instance D.Distribution TimeOfOriginNearCriticalDistribution where
cumulative = cumulative
cumulative :: TimeOfOriginNearCriticalDistribution -> Time -> Double
cumulative (TONCD n' l m) t
| t <= 0 = 0
| otherwise = t1 + t2
where d = l - m
n = fromIntegral n'
t1 = (t*l/(1.0 + t*l)) ** n
t2 = (n * t * t1) * d / (2.0 * (1.0 + t*l))
instance D.ContDistr TimeOfOriginNearCriticalDistribution where
density = density
quantile = quantile
density :: TimeOfOriginNearCriticalDistribution -> Time -> Double
density (TONCD n' l m) t
| t < 0 = 0
| otherwise = nom/den
where n = fromIntegral n'
nom = n * (t*l/(1+t*l))**n * (2+(3+n)*t*l - (1+n)*t*m)
den = 2*t*(1+t*l)**2
quantile :: TimeOfOriginNearCriticalDistribution -> Double -> Time
quantile (TONCD n' l m) p
| p >= 0 && p <= 1 = t1 + t2nom/t2den
| otherwise =
error $ "PointProcess.quantile: p must be in [0,1] range. Got: " ++ show p ++ "."
where n = fromIntegral n'
t1 = - p**(1/n)/((-1+p**(1/n))*l)
t2nom = p**(2/n)*(m-l)
t2den = 2*(-1+p**(1/n))**2 * l**2
instance D.ContGen TimeOfOriginNearCriticalDistribution where
genContVar = D.genContinuous