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|
{-# LANGUAGE DeriveDataTypeable #-}
-- |
-- Module : Statistics.Distribution.Geometric
-- Copyright : (c) 2009 Bryan O'Sullivan
-- License : BSD3
--
-- Maintainer : bos@serpentine.com
-- Stability : experimental
-- Portability : portable
--
-- The Geometric distribution. This is the probability distribution of
-- the number of Bernoulli trials needed to get one success, supported
-- on the set [1,2..].
--
-- This distribution is sometimes referred to as the /shifted/
-- geometric distribution, to distinguish it from a variant measuring
-- the number of failures before the first success, defined over the
-- set [0,1..].
module Statistics.Distribution.Geometric
(
GeometricDistribution
-- * Constructors
, geometric
-- ** Accessors
, gdSuccess
) where
import Data.Typeable (Typeable)
import qualified Statistics.Distribution as D
newtype GeometricDistribution = GD {
gdSuccess :: Double
} deriving (Eq, Read, Show, Typeable)
instance D.Distribution GeometricDistribution where
cumulative = cumulative
instance D.DiscreteDistr GeometricDistribution where
probability = probability
instance D.Mean GeometricDistribution where
mean (GD s) = 1 / s
{-# INLINE mean #-}
instance D.Variance GeometricDistribution where
variance (GD s) = (1 - s) / (s * s)
{-# INLINE variance #-}
instance D.MaybeMean GeometricDistribution where
maybeMean = Just . D.mean
instance D.MaybeVariance GeometricDistribution where
maybeStdDev = Just . D.stdDev
maybeVariance = Just . D.variance
-- | Create geometric distribution.
geometric :: Double -- ^ Success rate
-> GeometricDistribution
geometric x
| x >= 0 && x <= 1 = GD x
| otherwise =
error $ "Statistics.Distribution.Geometric.geometric: probability must be in [0,1] range. Got " ++ show x
{-# INLINE geometric #-}
probability :: GeometricDistribution -> Int -> Double
probability (GD s) n | n < 1 = 0
| otherwise = s * (1-s) ** (fromIntegral n - 1)
{-# INLINE probability #-}
cumulative :: GeometricDistribution -> Double -> Double
cumulative (GD s) x | x < 1 = 0
| otherwise = 1 - (1-s) ^ (floor x :: Int)
{-# INLINE cumulative #-}
|
