{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveGeneric #-}

-- |
--   Module      :  ELynx.Tree.Distribution.BirthDeathCritical
--   Description :  Birth and death distribution
--   Copyright   :  2021 Dominik Schrempf
--   License     :  GPL-3.0-or-later
--
--   Maintainer  :  dominik.schrempf@gmail.com
--   Stability   :  unstable
--   Portability :  portable
--
-- Creation date: Tue Feb 13 13:16:18 2018.
--
-- See Gernhard, T. (2008). The conditioned reconstructed process. Journal of
-- Theoretical Biology, 253(4), 769–778. http://doi.org/10.1016/j.jtbi.2008.04.005.
--
-- Distribution of the values of the point process such that it corresponds to
-- reconstructed trees under the birth and death process; critical birth and death
-- process with lambda=mu.
module ELynx.Tree.Distribution.BirthDeathCritical
  ( BirthDeathCriticalDistribution (..),
    cumulative,
    density,
    quantile,
  )
where

import Data.Data
  ( Data,
    Typeable,
  )
import ELynx.Tree.Distribution.Types
import GHC.Generics (Generic)
import qualified Statistics.Distribution as D

-- | Distribution of the values of the point process such that it corresponds to
-- a reconstructed tree of the birth and death process.
data BirthDeathCriticalDistribution = BDCD
  { -- | Time to origin of the tree.
    bdcdTOr :: Time,
    -- | Birth and death rate.
    bdcdLa :: Rate
  }
  deriving (Eq, Typeable, Data, Generic)

instance D.Distribution BirthDeathCriticalDistribution where
  cumulative = cumulative

-- | Cumulative distribution function section 2.1.2, second formula.
cumulative :: BirthDeathCriticalDistribution -> Time -> Double
cumulative (BDCD t l) x
  | x <= 0 = 0
  | x > t = 1
  | otherwise = x / (1.0 + l * x) * (1.0 + l * t) / t

instance D.ContDistr BirthDeathCriticalDistribution where
  density = density
  quantile = quantile

-- | Density function section 2.1.2, first formula.
density :: BirthDeathCriticalDistribution -> Time -> Double
density (BDCD t l) x
  | x < 0 = 0
  | x > t = 0
  | otherwise = (1.0 + l * t) / (t * (1.0 + l * x) ** 2)

-- | Inverted cumulative probability distribution 'cumulative'. See also
-- 'D.ContDistr'.
quantile :: BirthDeathCriticalDistribution -> Double -> Time
quantile (BDCD t l) p
  | p >= 0 && p <= 1 =
      res
  | otherwise =
      error $
        "PointProcess.quantile: p must be in [0,1] range. Got: "
          ++ show p
          ++ "."
  where
    res = p * t / (1 + l * t - l * p * t)

instance D.ContGen BirthDeathCriticalDistribution where
  genContVar = D.genContinuous