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|
{-# LANGUAGE DeriveDataTypeable, DeriveGeneric, FlexibleContexts,
FlexibleInstances, UndecidableInstances #-}
-- |
-- Module : Statistics.Distribution.Transform
-- Copyright : (c) 2013 John McDonnell;
-- License : BSD3
--
-- Maintainer : bos@serpentine.com
-- Stability : experimental
-- Portability : portable
--
-- Transformations over distributions
module Statistics.Distribution.Transform
(
LinearTransform (..)
, linTransFixedPoint
, scaleAround
) where
import Data.Aeson (FromJSON, ToJSON)
import Data.Binary (Binary)
import Data.Binary (put, get)
import Data.Data (Data, Typeable)
import GHC.Generics (Generic)
import qualified Statistics.Distribution as D
-- | Linear transformation applied to distribution.
--
-- > LinearTransform μ σ _
-- > x' = μ + σ·x
data LinearTransform d = LinearTransform
{ linTransLocation :: {-# UNPACK #-} !Double
-- ^ Location parameter.
, linTransScale :: {-# UNPACK #-} !Double
-- ^ Scale parameter.
, linTransDistr :: d
-- ^ Distribution being transformed.
} deriving (Eq, Show, Read, Typeable, Data, Generic)
instance (FromJSON d) => FromJSON (LinearTransform d)
instance (ToJSON d) => ToJSON (LinearTransform d)
instance (Binary d) => Binary (LinearTransform d) where
get = LinearTransform <$> get <*> get <*> get
put (LinearTransform x y z) = put x >> put y >> put z
-- | Apply linear transformation to distribution.
scaleAround :: Double -- ^ Fixed point
-> Double -- ^ Scale parameter
-> d -- ^ Distribution
-> LinearTransform d
scaleAround x0 sc = LinearTransform (x0 * (1 - sc)) sc
-- | Get fixed point of linear transformation
linTransFixedPoint :: LinearTransform d -> Double
linTransFixedPoint (LinearTransform loc sc _) = loc / (1 - sc)
instance Functor LinearTransform where
fmap f (LinearTransform loc sc dist) = LinearTransform loc sc (f dist)
instance D.Distribution d => D.Distribution (LinearTransform d) where
cumulative (LinearTransform loc sc dist) x = D.cumulative dist $ (x-loc) / sc
instance D.ContDistr d => D.ContDistr (LinearTransform d) where
density (LinearTransform loc sc dist) x = D.density dist ((x-loc) / sc) / sc
logDensity (LinearTransform loc sc dist) x = D.logDensity dist ((x-loc) / sc) - log sc
quantile (LinearTransform loc sc dist) p = loc + sc * D.quantile dist p
complQuantile (LinearTransform loc sc dist) p = loc + sc * D.complQuantile dist p
instance D.MaybeMean d => D.MaybeMean (LinearTransform d) where
maybeMean (LinearTransform loc _ dist) = (+loc) <$> D.maybeMean dist
instance (D.Mean d) => D.Mean (LinearTransform d) where
mean (LinearTransform loc _ dist) = loc + D.mean dist
instance D.MaybeVariance d => D.MaybeVariance (LinearTransform d) where
maybeVariance (LinearTransform _ sc dist) = (*(sc*sc)) <$> D.maybeVariance dist
maybeStdDev (LinearTransform _ sc dist) = (*sc) <$> D.maybeStdDev dist
instance (D.Variance d) => D.Variance (LinearTransform d) where
variance (LinearTransform _ sc dist) = sc * sc * D.variance dist
stdDev (LinearTransform _ sc dist) = sc * D.stdDev dist
instance (D.MaybeEntropy d) => D.MaybeEntropy (LinearTransform d) where
maybeEntropy (LinearTransform _ _ dist) = D.maybeEntropy dist
instance (D.Entropy d) => D.Entropy (LinearTransform d) where
entropy (LinearTransform _ _ dist) = D.entropy dist
instance D.ContGen d => D.ContGen (LinearTransform d) where
genContVar (LinearTransform loc sc d) g = do
x <- D.genContVar d g
return $! loc + sc * x
|
