{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveGeneric #-}
module ELynx.Distribution.BirthDeathNearlyCritical
( BirthDeathNearlyCriticalDistribution (..),
cumulative,
density,
quantile,
)
where
import Data.Data
( Data,
Typeable,
)
import ELynx.Distribution.Types
import GHC.Generics (Generic)
import qualified Statistics.Distribution as D
data BirthDeathNearlyCriticalDistribution = BDNCD
{
bdncdTOr :: Time,
bdncdLa :: Rate,
bdncdMu :: Rate
}
deriving (Eq, Typeable, Data, Generic)
instance D.Distribution BirthDeathNearlyCriticalDistribution where
cumulative = cumulative
cumulative :: BirthDeathNearlyCriticalDistribution -> Time -> Double
cumulative (BDNCD t l m) s
| s <= 0 = 0
| s > t = 1
| otherwise = o0 + o1
where
o0 = s * (1.0 + t * l) / t / (1.0 + s * l)
o1 = (- s * s + s * t) * (m - l) / (2.0 * t * (1.0 + s * l) ** 2)
instance D.ContDistr BirthDeathNearlyCriticalDistribution where
density = density
quantile = quantile
density :: BirthDeathNearlyCriticalDistribution -> Time -> Double
density (BDNCD t l m) s
| s < 0 = 0
| s > t = 0
| otherwise = o0 + o1
where
o0 = (1.0 + t * l) / (t * (1.0 + s * l) ** 2)
o1 = (-2.0 * s + t - s * t * l) * (m - l) / (2.0 * t * (1.0 + s * l) ** 3)
quantile :: BirthDeathNearlyCriticalDistribution -> Double -> Time
quantile (BDNCD t l m) p
| p >= 0 && p <= 1 =
res
| otherwise =
error $
"PointProcess.quantile: p must be in [0,1] range. Got: "
++ show p
++ "."
where
den = l * (-3.0 + 2.0 * t * (-1.0 + p) * l) + m
t1 = (2.0 + t * (l - 4.0 * p * l + m)) / den
t2Nom =
4.0
+ t
* ( l
* (4.0 + t * l + 8.0 * p * (1.0 + t * l))
+ 2.0
* (2.0 + t * l - 4.0 * p * (1.0 + t * l))
* m
+ t
* m
* m
)
t2 = t2Nom / (den ** 2)
res = 0.5 * (t1 + sqrt t2)
instance D.ContGen BirthDeathNearlyCriticalDistribution where
genContVar = D.genContinuous