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{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE DeriveDataTypeable, DeriveGeneric #-}
-- |
-- Module : Statistics.Distribution.Uniform
-- Copyright : (c) 2011 Aleksey Khudyakov
-- License : BSD3
--
-- Maintainer : bos@serpentine.com
-- Stability : experimental
-- Portability : portable
--
-- Variate distributed uniformly in the interval.
module Statistics.Distribution.Uniform
(
UniformDistribution
-- * Constructors
, uniformDistr
, uniformDistrE
-- ** Accessors
, uniformA
, uniformB
) where
import Control.Applicative
import Data.Aeson (FromJSON(..), ToJSON, Value(..), (.:))
import Data.Binary (Binary(..))
import Data.Data (Data, Typeable)
import System.Random.Stateful (uniformRM)
import GHC.Generics (Generic)
import qualified Statistics.Distribution as D
import Statistics.Internal
-- | Uniform distribution from A to B
data UniformDistribution = UniformDistribution {
uniformA :: {-# UNPACK #-} !Double -- ^ Low boundary of distribution
, uniformB :: {-# UNPACK #-} !Double -- ^ Upper boundary of distribution
} deriving (Eq, Typeable, Data, Generic)
instance Show UniformDistribution where
showsPrec i (UniformDistribution a b) = defaultShow2 "uniformDistr" a b i
instance Read UniformDistribution where
readPrec = defaultReadPrecM2 "uniformDistr" uniformDistrE
instance ToJSON UniformDistribution
instance FromJSON UniformDistribution where
parseJSON (Object v) = do
a <- v .: "uniformA"
b <- v .: "uniformB"
maybe (fail errMsg) return $ uniformDistrE a b
parseJSON _ = empty
instance Binary UniformDistribution where
put (UniformDistribution x y) = put x >> put y
get = do
a <- get
b <- get
maybe (fail errMsg) return $ uniformDistrE a b
-- | Create uniform distribution.
uniformDistr :: Double -> Double -> UniformDistribution
uniformDistr a b = maybe (error errMsg) id $ uniformDistrE a b
-- | Create uniform distribution.
uniformDistrE :: Double -> Double -> Maybe UniformDistribution
uniformDistrE a b
| b < a = Just $ UniformDistribution b a
| a < b = Just $ UniformDistribution a b
| otherwise = Nothing
-- NOTE: failure is in default branch to guard against NaNs.
errMsg :: String
errMsg = "Statistics.Distribution.Uniform.uniform: wrong parameters"
instance D.Distribution UniformDistribution where
cumulative (UniformDistribution a b) x
| x < a = 0
| x > b = 1
| otherwise = (x - a) / (b - a)
instance D.ContDistr UniformDistribution where
density (UniformDistribution a b) x
| x < a = 0
| x > b = 0
| otherwise = 1 / (b - a)
quantile (UniformDistribution a b) p
| p >= 0 && p <= 1 = a + (b - a) * p
| otherwise =
error $ "Statistics.Distribution.Uniform.quantile: p must be in [0,1] range. Got: "++show p
complQuantile (UniformDistribution a b) p
| p >= 0 && p <= 1 = b + (a - b) * p
| otherwise =
error $ "Statistics.Distribution.Uniform.complQuantile: p must be in [0,1] range. Got: "++show p
instance D.Mean UniformDistribution where
mean (UniformDistribution a b) = 0.5 * (a + b)
instance D.Variance UniformDistribution where
-- NOTE: 1/sqrt 12 is not constant folded (#4101) so it's written as
-- numerical constant. (Also FIXME!)
stdDev (UniformDistribution a b) = 0.2886751345948129 * (b - a)
variance (UniformDistribution a b) = d * d / 12 where d = b - a
instance D.MaybeMean UniformDistribution where
maybeMean = Just . D.mean
instance D.MaybeVariance UniformDistribution where
maybeStdDev = Just . D.stdDev
instance D.Entropy UniformDistribution where
entropy (UniformDistribution a b) = log (b - a)
instance D.MaybeEntropy UniformDistribution where
maybeEntropy = Just . D.entropy
instance D.ContGen UniformDistribution where
genContVar (UniformDistribution a b) = uniformRM (a,b)
|
