{-# 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. There are two variants of -- distribution. First is the probability distribution of the number -- of Bernoulli trials needed to get one success, supported on the set -- [1,2..] ('GeometricDistribution'). Sometimes it's referred to as -- the /shifted/ geometric distribution to distinguish from another -- one. -- -- Second variant is probability distribution of the number of -- failures before first success, defined over the set [0,1..] -- ('GeometricDistribution0'). module Statistics.Distribution.Geometric ( GeometricDistribution , GeometricDistribution0 -- * Constructors , geometric , geometric0 -- ** Accessors , gdSuccess , gdSuccess0 ) where import Data.Aeson (FromJSON, ToJSON) import Control.Applicative ((<\$>)) import Control.Monad (liftM) import Data.Binary (Binary) import Data.Binary (put, get) import Data.Data (Data, Typeable) import GHC.Generics (Generic) import Numeric.MathFunctions.Constants (m_pos_inf, m_neg_inf) import qualified Statistics.Distribution as D import qualified System.Random.MWC.Distributions as MWC ---------------------------------------------------------------- -- Distribution over [1..] newtype GeometricDistribution = GD { gdSuccess :: Double } deriving (Eq, Read, Show, Typeable, Data, Generic) instance FromJSON GeometricDistribution instance ToJSON GeometricDistribution instance Binary GeometricDistribution where get = GD <\$> get put (GD x) = put x instance D.Distribution GeometricDistribution where cumulative = cumulative instance D.DiscreteDistr GeometricDistribution where probability (GD s) n | n < 1 = 0 | otherwise = s * (1-s) ** (fromIntegral n - 1) logProbability (GD s) n | n < 1 = m_neg_inf | otherwise = log s + log (1-s) * (fromIntegral n - 1) instance D.Mean GeometricDistribution where mean (GD s) = 1 / s instance D.Variance GeometricDistribution where variance (GD s) = (1 - s) / (s * s) instance D.MaybeMean GeometricDistribution where maybeMean = Just . D.mean instance D.MaybeVariance GeometricDistribution where maybeStdDev = Just . D.stdDev maybeVariance = Just . D.variance instance D.Entropy GeometricDistribution where entropy (GD s) | s == 0 = m_pos_inf | s == 1 = 0 | otherwise = negate \$ (s * log s + (1-s) * log (1-s)) / s instance D.MaybeEntropy GeometricDistribution where maybeEntropy = Just . D.entropy instance D.DiscreteGen GeometricDistribution where genDiscreteVar (GD s) g = MWC.geometric1 s g instance D.ContGen GeometricDistribution where genContVar d g = fromIntegral `liftM` D.genDiscreteVar d g -- | 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 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) ---------------------------------------------------------------- -- Distribution over [0..] newtype GeometricDistribution0 = GD0 { gdSuccess0 :: Double } deriving (Eq, Read, Show, Typeable, Data, Generic) instance FromJSON GeometricDistribution0 instance ToJSON GeometricDistribution0 instance Binary GeometricDistribution0 where get = GD0 <\$> get put (GD0 x) = put x instance D.Distribution GeometricDistribution0 where cumulative (GD0 s) x = cumulative (GD s) (x + 1) instance D.DiscreteDistr GeometricDistribution0 where probability (GD0 s) n = D.probability (GD s) (n + 1) logProbability (GD0 s) n = D.logProbability (GD s) (n + 1) instance D.Mean GeometricDistribution0 where mean (GD0 s) = 1 / s - 1 instance D.Variance GeometricDistribution0 where variance (GD0 s) = D.variance (GD s) instance D.MaybeMean GeometricDistribution0 where maybeMean = Just . D.mean instance D.MaybeVariance GeometricDistribution0 where maybeStdDev = Just . D.stdDev maybeVariance = Just . D.variance instance D.Entropy GeometricDistribution0 where entropy (GD0 s) = D.entropy (GD s) instance D.MaybeEntropy GeometricDistribution0 where maybeEntropy = Just . D.entropy instance D.DiscreteGen GeometricDistribution0 where genDiscreteVar (GD0 s) g = MWC.geometric0 s g instance D.ContGen GeometricDistribution0 where genContVar d g = fromIntegral `liftM` D.genDiscreteVar d g -- | Create geometric distribution. geometric0 :: Double -- ^ Success rate -> GeometricDistribution0 geometric0 x | x >= 0 && x <= 1 = GD0 x | otherwise = error \$ "Statistics.Distribution.Geometric.geometric: probability must be in [0,1] range. Got " ++ show x