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{-# LANGUAGE DeriveDataTypeable #-}
-- |
-- Module : Statistics.Distribution.Exponential
-- Copyright : (c) 2009 Bryan O'Sullivan
-- License : BSD3
--
-- Maintainer : bos@serpentine.com
-- Stability : experimental
-- Portability : portable
--
-- The exponential distribution. This is the continunous probability
-- distribution of the times between events in a poisson process, in
-- which events occur continuously and independently at a constant
-- average rate.
module Statistics.Distribution.Exponential
(
ExponentialDistribution
-- * Constructors
, exponential
, exponentialFromSample
-- * Accessors
, edLambda
) where
import Data.Typeable (Typeable)
import qualified Statistics.Distribution as D
import qualified Statistics.Sample as S
import qualified System.Random.MWC.Distributions as MWC
import Statistics.Types (Sample)
newtype ExponentialDistribution = ED {
edLambda :: Double
} deriving (Eq, Read, Show, Typeable)
instance D.Distribution ExponentialDistribution where
cumulative = cumulative
complCumulative = complCumulative
instance D.ContDistr ExponentialDistribution where
density = density
quantile = quantile
instance D.Mean ExponentialDistribution where
mean (ED l) = 1 / l
{-# INLINE mean #-}
instance D.Variance ExponentialDistribution where
variance (ED l) = 1 / (l * l)
{-# INLINE variance #-}
instance D.MaybeMean ExponentialDistribution where
maybeMean = Just . D.mean
instance D.MaybeVariance ExponentialDistribution where
maybeStdDev = Just . D.stdDev
maybeVariance = Just . D.variance
instance D.ContGen ExponentialDistribution where
genContVar = MWC.exponential . edLambda
cumulative :: ExponentialDistribution -> Double -> Double
cumulative (ED l) x | x <= 0 = 0
| otherwise = 1 - exp (-l * x)
{-# INLINE cumulative #-}
complCumulative :: ExponentialDistribution -> Double -> Double
complCumulative (ED l) x | x <= 0 = 1
| otherwise = exp (-l * x)
{-# INLINE complCumulative #-}
density :: ExponentialDistribution -> Double -> Double
density (ED l) x | x < 0 = 0
| otherwise = l * exp (-l * x)
{-# INLINE density #-}
quantile :: ExponentialDistribution -> Double -> Double
quantile (ED l) p
| p == 1 = 1 / 0
| p >= 0 && p < 1 = -log (1 - p) / l
| otherwise =
error $ "Statistics.Distribution.Exponential.quantile: p must be in [0,1] range. Got: "++show p
{-# INLINE quantile #-}
-- | Create an exponential distribution.
exponential :: Double -- ^ λ (scale) parameter.
-> ExponentialDistribution
exponential l
| l <= 0 =
error $ "Statistics.Distribution.Exponential.exponential: scale parameter must be positive. Got " ++ show l
| otherwise = ED l
{-# INLINE exponential #-}
-- | Create exponential distribution from sample. No tests are made to
-- check whether it truly is exponential.
exponentialFromSample :: Sample -> ExponentialDistribution
exponentialFromSample = ED . S.mean
{-# INLINE exponentialFromSample #-}
|
