    {-# 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