```{-# LANGUAGE DeriveDataTypeable, DeriveGeneric #-}
-- |
-- 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.Binary (Binary)
import Data.Data (Data, Typeable)
import GHC.Generics (Generic)
import qualified Statistics.Distribution as D

newtype GeometricDistribution = GD {
gdSuccess :: Double
} deriving (Eq, Read, Show, Typeable, Data, Generic)

instance Binary GeometricDistribution

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
| isInfinite x = 1
| isNaN      x = error "Statistics.Distribution.Geometric.cumulative: NaN input"
| otherwise    = 1 - (1-s) ^ (floor x :: Int)
{-# INLINE cumulative #-}
```