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 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 ``` ``````{-# LANGUAGE OverloadedStrings #-} {-# 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 , geometricE , geometric0 , geometric0E -- ** Accessors , gdSuccess , gdSuccess0 ) where import Control.Applicative import Control.Monad (liftM) import Data.Aeson (FromJSON(..), ToJSON, Value(..), (.:)) import Data.Binary (Binary(..)) import Data.Data (Data, Typeable) import GHC.Generics (Generic) import Numeric.MathFunctions.Constants (m_pos_inf, m_neg_inf) import Numeric.SpecFunctions (log1p,expm1) import qualified System.Random.MWC.Distributions as MWC import qualified Statistics.Distribution as D import Statistics.Internal ---------------------------------------------------------------- -- | Distribution over [1..] newtype GeometricDistribution = GD { gdSuccess :: Double } deriving (Eq, Typeable, Data, Generic) instance Show GeometricDistribution where showsPrec i (GD x) = defaultShow1 "geometric" x i instance Read GeometricDistribution where readPrec = defaultReadPrecM1 "geometric" geometricE instance ToJSON GeometricDistribution instance FromJSON GeometricDistribution where parseJSON (Object v) = do x <- v .: "gdSuccess" maybe (fail \$ errMsg x) return \$ geometricE x parseJSON _ = empty instance Binary GeometricDistribution where put (GD x) = put x get = do x <- get maybe (fail \$ errMsg x) return \$ geometricE x instance D.Distribution GeometricDistribution where cumulative = cumulative complCumulative = complCumulative 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 cumulative :: GeometricDistribution -> Double -> Double cumulative (GD s) x | x < 1 = 0 | isInfinite x = 1 | isNaN x = error "Statistics.Distribution.Geometric.cumulative: NaN input" | otherwise = negate \$ expm1 \$ fromIntegral (floor x :: Int) * log1p (-s) complCumulative :: GeometricDistribution -> Double -> Double complCumulative (GD s) x | x < 1 = 1 | isInfinite x = 0 | isNaN x = error "Statistics.Distribution.Geometric.cumulative: NaN input" | otherwise = exp \$ fromIntegral (floor x :: Int) * log1p (-s) -- | Create geometric distribution. geometric :: Double -- ^ Success rate -> GeometricDistribution geometric x = maybe (error \$ errMsg x) id \$ geometricE x -- | Create geometric distribution. geometricE :: Double -- ^ Success rate -> Maybe GeometricDistribution geometricE x | x >= 0 && x <= 1 = Just (GD x) | otherwise = Nothing errMsg :: Double -> String errMsg x = "Statistics.Distribution.Geometric.geometric: probability must be in [0,1] range. Got " ++ show x ---------------------------------------------------------------- -- | Distribution over [0..] newtype GeometricDistribution0 = GD0 { gdSuccess0 :: Double } deriving (Eq, Typeable, Data, Generic) instance Show GeometricDistribution0 where showsPrec i (GD0 x) = defaultShow1 "geometric0" x i instance Read GeometricDistribution0 where readPrec = defaultReadPrecM1 "geometric0" geometric0E instance ToJSON GeometricDistribution0 instance FromJSON GeometricDistribution0 where parseJSON (Object v) = do x <- v .: "gdSuccess0" maybe (fail \$ errMsg x) return \$ geometric0E x parseJSON _ = empty instance Binary GeometricDistribution0 where put (GD0 x) = put x get = do x <- get maybe (fail \$ errMsg x) return \$ geometric0E x instance D.Distribution GeometricDistribution0 where cumulative (GD0 s) x = cumulative (GD s) (x + 1) complCumulative (GD0 s) x = complCumulative (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 = maybe (error \$ errMsg0 x) id \$ geometric0E x -- | Create geometric distribution. geometric0E :: Double -- ^ Success rate -> Maybe GeometricDistribution0 geometric0E x | x >= 0 && x <= 1 = Just (GD0 x) | otherwise = Nothing errMsg0 :: Double -> String errMsg0 x = "Statistics.Distribution.Geometric.geometric0: probability must be in [0,1] range. Got " ++ show x ``````