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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
, fromLambda
, fromSample
-- * Accessors
, edLambda
) where
import Data.Typeable (Typeable)
import qualified Statistics.Distribution as D
import qualified Statistics.Sample as S
import Statistics.Types (Sample)
newtype ExponentialDistribution = ED {
edLambda :: Double
} deriving (Eq, Read, Show, Typeable)
instance D.Distribution ExponentialDistribution where
density (ED l) x = l * exp (-l * x)
{-# INLINE density #-}
cumulative (ED l) x = 1 - exp (-l * x)
{-# INLINE cumulative #-}
quantile (ED l) p = -log (1 - p) / l
{-# INLINE quantile #-}
instance D.Variance ExponentialDistribution where
variance (ED l) = 1 / (l * l)
{-# INLINE variance #-}
instance D.Mean ExponentialDistribution where
mean (ED l) = 1 / l
{-# INLINE mean #-}
fromLambda :: Double -- ^ λ (scale) parameter.
-> ExponentialDistribution
fromLambda = ED
{-# INLINE fromLambda #-}
fromSample :: Sample -> ExponentialDistribution
fromSample = ED . S.mean
{-# INLINE fromSample #-}
|
