module Statistics.Distribution.Geometric
(
GeometricDistribution
, GeometricDistribution0
, geometric
, geometric0
, gdSuccess
, gdSuccess0
) where
import Data.Aeson (FromJSON, ToJSON)
import Control.Applicative ((<$>))
import Control.Monad (liftM)
import Data.Binary (Binary)
import Data.Binary (put, get)
import Data.Data (Data, Typeable)
import GHC.Generics (Generic)
import Numeric.MathFunctions.Constants (m_pos_inf, m_neg_inf)
import qualified Statistics.Distribution as D
import qualified System.Random.MWC.Distributions as MWC
newtype GeometricDistribution = GD {
gdSuccess :: Double
} deriving (Eq, Read, Show, Typeable, Data, Generic)
instance FromJSON GeometricDistribution
instance ToJSON GeometricDistribution
instance Binary GeometricDistribution where
get = GD <$> 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 * (1s) ** (fromIntegral n 1)
logProbability (GD s) n
| n < 1 = m_neg_inf
| otherwise = log s + log (1s) * (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 + (1s) * log (1s)) / 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
geometric :: Double
-> 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 (1s) ^ (floor x :: Int)
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
geometric0 :: Double
-> 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