packages feed

statistics 0.10.5.2 → 0.11.0.0

raw patch · 46 files changed

+769/−573 lines, 46 filesdep ~binarydep ~math-functions

Dependency ranges changed: binary, math-functions

Files

ChangeLog view
@@ -1,3 +1,18 @@+-*- text -*-++Changes in 0.10.6.0++  * The Estimator type has become an algebraic data type.  This allows+    the jackknife function to potentially use more efficient jackknife+    implementations.++  * jackknifeMean, jackknifeStdDev, jackknifeVariance,+    jackknifeVarianceUnb: new functions.  These have O(n) cost instead+    of the O(n^2) cost of the standard jackknife.++  * The mean function has been renamed to welfordMean; a new+    implementation of mean has better numerical accuracy in almost all+    cases.  Changes in 0.10.5.2
Statistics/Autocorrelation.hs view
@@ -17,7 +17,9 @@     , autocorrelation     ) where +import Prelude hiding (sum) import Statistics.Sample (mean)+import Statistics.Sample.Internal (sum) import qualified Data.Vector.Generic as G  -- | Compute the autocovariance of a sample, i.e. the covariance of@@ -25,7 +27,7 @@ autocovariance :: (G.Vector v Double, G.Vector v Int) => v Double -> v Double autocovariance a = G.map f . G.enumFromTo 0 $ l-2   where-    f k = G.sum (G.zipWith (*) (G.take (l-k) c) (G.slice k (l-k) c))+    f k = sum (G.zipWith (*) (G.take (l-k) c) (G.slice k (l-k) c))           / fromIntegral l     c   = G.map (subtract (mean a)) a     l   = G.length a
Statistics/Distribution.hs view
@@ -32,14 +32,14 @@     , sumProbabilities     ) where -import Control.Applicative     ((<$>), Applicative(..))+import Control.Applicative ((<$>), Applicative(..)) import Control.Monad.Primitive (PrimMonad,PrimState)-+import Prelude hiding (sum)+import Statistics.Sample.Internal (sum)+import System.Random.MWC (Gen, uniform) import qualified Data.Vector.Unboxed as U-import System.Random.MWC  - -- | Type class common to all distributions. Only c.d.f. could be -- defined for both discrete and continous distributions. class Distribution d where@@ -141,7 +141,7 @@ class (Distribution d) => MaybeEntropy d where   -- | Returns the entropy of a distribution, in nats, if such is defined.   maybeEntropy :: d -> Maybe Double-  + -- | Type class for distributions with entropy, meaning Shannon --   entropy in the case of a discrete distribution, or differential --   entropy in the case of a continuous one.  If the distribution has@@ -178,7 +178,7 @@ -- bisection with the given guess as a starting point.  The upper and -- lower bounds specify the interval in which the probability -- distribution reaches the value /p/.-findRoot :: ContDistr d => +findRoot :: ContDistr d =>             d                   -- ^ Distribution          -> Double              -- ^ Probability /p/          -> Double              -- ^ Initial guess@@ -207,7 +207,7 @@ -- | Sum probabilities in inclusive interval. sumProbabilities :: DiscreteDistr d => d -> Int -> Int -> Double sumProbabilities d low hi =-  -- Return value is forced to be less than 1 to guard againist roundoff errors. +  -- Return value is forced to be less than 1 to guard againist roundoff errors.   -- ATTENTION! this check should be removed for testing or it could mask bugs.-  min 1 . U.sum . U.map (probability d) $ U.enumFromTo low hi+  min 1 . sum . U.map (probability d) $ U.enumFromTo low hi {-# INLINE sumProbabilities #-}
Statistics/Distribution/Beta.hs view
@@ -27,6 +27,8 @@   incompleteBeta, invIncompleteBeta, logBeta, digamma) import Numeric.MathFunctions.Constants (m_NaN) import qualified Statistics.Distribution as D+import Data.Binary (put, get)+import Control.Applicative ((<$>), (<*>))  -- | The beta distribution data BetaDistribution = BD@@ -36,7 +38,9 @@    -- ^ Beta shape parameter  } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary BetaDistribution+instance Binary BetaDistribution where+    put (BD x y) = put x >> put y+    get = BD <$> get <*> get  -- | Create beta distribution. Both shape parameters must be positive. betaDistr :: Double             -- ^ Shape parameter alpha@@ -85,12 +89,12 @@  instance D.Entropy BetaDistribution where   entropy (BD a b) =-    logBeta a b +    logBeta a b     - (a-1) * digamma a     - (b-1) * digamma b     + (a+b-2) * digamma (a+b)   {-# INLINE entropy #-}-    + instance D.MaybeEntropy BetaDistribution where   maybeEntropy = Just . D.entropy   {-# INLINE maybeEntropy #-}
Statistics/Distribution/Binomial.hs view
@@ -30,6 +30,8 @@ import qualified Statistics.Distribution.Poisson.Internal as I import Numeric.SpecFunctions (choose,incompleteBeta) import Numeric.MathFunctions.Constants (m_epsilon)+import Data.Binary (put, get)+import Control.Applicative ((<$>), (<*>))   -- | The binomial distribution.@@ -40,7 +42,9 @@     -- ^ Probability.     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary BinomialDistribution+instance Binary BinomialDistribution where+    put (BD x y) = put x >> put y+    get = BD <$> get <*> get  instance D.Distribution BinomialDistribution where     cumulative = cumulative@@ -99,7 +103,7 @@ {-# INLINE variance #-}  directEntropy :: BinomialDistribution -> Double-directEntropy d@(BD n _) =   +directEntropy d@(BD n _) =   negate . sum $   takeWhile (< negate m_epsilon) $   dropWhile (not . (< negate m_epsilon)) $
Statistics/Distribution/CauchyLorentz.hs view
@@ -25,6 +25,8 @@ import Data.Data (Data, Typeable) import GHC.Generics (Generic) import qualified Statistics.Distribution as D+import Data.Binary (put, get)+import Control.Applicative ((<$>), (<*>))  -- | Cauchy-Lorentz distribution. data CauchyDistribution = CD {@@ -39,7 +41,9 @@   }   deriving (Eq, Show, Read, Typeable, Data, Generic) -instance Binary CauchyDistribution+instance Binary CauchyDistribution where+    put (CD x y) = put x >> put y+    get = CD <$> get <*> get  -- | Cauchy distribution cauchyDistribution :: Double    -- ^ Central point@@ -72,6 +76,6 @@  instance D.Entropy CauchyDistribution where   entropy (CD _ s) = log s + log (4*pi)-    + instance D.MaybeEntropy CauchyDistribution where   maybeEntropy = Just . D.entropy
Statistics/Distribution/ChiSquared.hs view
@@ -26,13 +26,16 @@  import qualified Statistics.Distribution         as D import qualified System.Random.MWC.Distributions as MWC+import Data.Binary (put, get)   -- | Chi-squared distribution newtype ChiSquared = ChiSquared Int                      deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary ChiSquared+instance Binary ChiSquared where+    get = fmap ChiSquared get+    put (ChiSquared x) = put x  -- | Get number of degrees of freedom chiSquaredNDF :: ChiSquared -> Int@@ -69,12 +72,12 @@ instance D.MaybeVariance ChiSquared where     maybeStdDev   = Just . D.stdDev     maybeVariance = Just . D.variance-    + instance D.Entropy ChiSquared where   entropy (ChiSquared ndf) =     let kHalf = 0.5 * fromIntegral ndf in-    kHalf -    + log 2 +    kHalf+    + log 2     + logGamma kHalf     + (1-kHalf) * digamma kHalf
Statistics/Distribution/Exponential.hs view
@@ -31,13 +31,16 @@ import qualified Statistics.Sample               as S import qualified System.Random.MWC.Distributions as MWC import Statistics.Types (Sample)+import Data.Binary (put, get)   newtype ExponentialDistribution = ED {       edLambda :: Double     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary ExponentialDistribution+instance Binary ExponentialDistribution where+    put = put . edLambda+    get = fmap ED get  instance D.Distribution ExponentialDistribution where     cumulative      = cumulative
Statistics/Distribution/FDistribution.hs view
@@ -23,6 +23,8 @@ import qualified Statistics.Distribution as D import Numeric.SpecFunctions (   logBeta, incompleteBeta, invIncompleteBeta, digamma)+import Data.Binary (put, get)+import Control.Applicative ((<$>), (<*>))   @@ -33,7 +35,9 @@                        }                    deriving (Eq, Show, Read, Typeable, Data, Generic) -instance Binary FDistribution+instance Binary FDistribution where+    get = F <$> get <*> get <*> get+    put (F x y z) = put x >> put y >> put z  fDistribution :: Int -> Int -> FDistribution fDistribution n m@@ -89,9 +93,9 @@   entropy (F n m _) =     let nHalf = 0.5 * n         mHalf = 0.5 * m in-    log (n/m) +    log (n/m)     + logBeta nHalf mHalf-    + (1 - nHalf) * digamma nHalf +    + (1 - nHalf) * digamma nHalf     - (1 + mHalf) * digamma mHalf     + (nHalf + mHalf) * digamma (nHalf + mHalf)
Statistics/Distribution/Gamma.hs view
@@ -25,14 +25,15 @@     , gdScale     ) where +import Control.Applicative ((<$>), (<*>)) import Data.Binary (Binary)+import Data.Binary (put, get) import Data.Data (Data, Typeable) import GHC.Generics (Generic) import Numeric.MathFunctions.Constants (m_pos_inf, m_NaN, m_neg_inf)-import Numeric.SpecFunctions (-  incompleteGamma, invIncompleteGamma, logGamma, digamma)-import Statistics.Distribution.Poisson.Internal  as Poisson-import qualified Statistics.Distribution         as D+import Numeric.SpecFunctions (incompleteGamma, invIncompleteGamma, logGamma, digamma)+import Statistics.Distribution.Poisson.Internal as Poisson+import qualified Statistics.Distribution as D import qualified System.Random.MWC.Distributions as MWC  -- | The gamma distribution.@@ -41,7 +42,9 @@     , gdScale :: {-# UNPACK #-} !Double -- ^ Scale parameter, &#977;.     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary GammaDistribution+instance Binary GammaDistribution where+    put (GD x y) = put x >> put y+    get = GD <$> get <*> get  -- | Create gamma distribution. Both shape and scale parameters must -- be positive.@@ -90,11 +93,11 @@  instance D.MaybeEntropy GammaDistribution where   maybeEntropy (GD a l)-    | a > 0 && l > 0 = +    | a > 0 && l > 0 =       Just $-      a -      + log l -      + logGamma a +      a+      + log l+      + logGamma a       + (1-a) * digamma a     | otherwise = Nothing
Statistics/Distribution/Geometric.hs view
@@ -30,12 +30,14 @@     , gdSuccess0     ) where -import Control.Monad  (liftM)-import Data.Binary    (Binary)-import Data.Data      (Data, Typeable)-import GHC.Generics   (Generic)-import Numeric.MathFunctions.Constants(m_pos_inf,m_neg_inf)-import qualified Statistics.Distribution         as D+import Control.Applicative ((<$>))+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  ----------------------------------------------------------------@@ -45,7 +47,9 @@       gdSuccess :: Double     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary GeometricDistribution+instance Binary GeometricDistribution where+    get = GD <$> get+    put (GD x) = put x  instance D.Distribution GeometricDistribution where     cumulative = cumulative@@ -115,7 +119,9 @@       gdSuccess0 :: Double     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary GeometricDistribution0+instance Binary GeometricDistribution0 where+    get = GD0 <$> get+    put (GD0 x) = put x  instance D.Distribution GeometricDistribution0 where     cumulative (GD0 s) x = cumulative (GD s) (x + 1)
Statistics/Distribution/Hypergeometric.hs view
@@ -33,6 +33,8 @@ import Numeric.MathFunctions.Constants (m_epsilon) import Numeric.SpecFunctions (choose) import qualified Statistics.Distribution as D+import Data.Binary (put, get)+import Control.Applicative ((<$>), (<*>))  data HypergeometricDistribution = HD {       hdM :: {-# UNPACK #-} !Int@@ -40,7 +42,9 @@     , hdK :: {-# UNPACK #-} !Int     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary HypergeometricDistribution+instance Binary HypergeometricDistribution where+    get = HD <$> get <*> get <*> get+    put (HD x y z) = put x >> put y >> put z  instance D.Distribution HypergeometricDistribution where     cumulative = cumulative@@ -63,7 +67,7 @@  instance D.Entropy HypergeometricDistribution where   entropy = directEntropy-  + instance D.MaybeEntropy HypergeometricDistribution where   maybeEntropy = Just . D.entropy
Statistics/Distribution/Normal.hs view
@@ -20,17 +20,18 @@     , standard     ) where +import Control.Applicative ((<$>), (<*>)) import Data.Binary (Binary)+import Data.Binary (put, get) import Data.Data (Data, Typeable) import GHC.Generics (Generic) import Numeric.MathFunctions.Constants (m_sqrt_2, m_sqrt_2_pi)-import Numeric.SpecFunctions           (erfc, invErfc)+import Numeric.SpecFunctions (erfc, invErfc) import qualified Statistics.Distribution as D-import qualified Statistics.Sample       as S+import qualified Statistics.Sample as S import qualified System.Random.MWC.Distributions as MWC  - -- | The normal distribution. data NormalDistribution = ND {       mean       :: {-# UNPACK #-} !Double@@ -39,7 +40,9 @@     , ndCdfDenom :: {-# UNPACK #-} !Double     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary NormalDistribution+instance Binary NormalDistribution where+    put (ND w x y z) = put w >> put x >> put y >> put z+    get = ND <$> get <*> get <*> get <*> get  instance D.Distribution NormalDistribution where     cumulative      = cumulative
Statistics/Distribution/Poisson.hs view
@@ -31,13 +31,16 @@ import qualified Statistics.Distribution.Poisson.Internal as I import Numeric.SpecFunctions (incompleteGamma,logFactorial) import Numeric.MathFunctions.Constants (m_neg_inf)+import Data.Binary (put, get)   newtype PoissonDistribution = PD {       poissonLambda :: Double     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary PoissonDistribution+instance Binary PoissonDistribution where+    get = fmap PD get+    put = put . poissonLambda  instance D.Distribution PoissonDistribution where     cumulative (PD lambda) x@@ -78,8 +81,9 @@ poisson :: Double -> PoissonDistribution poisson l   | l >=  0   = PD l-  | otherwise = error $ "Statistics.Distribution.Poisson.poisson:\-                        \ lambda must be non-negative. Got " ++ show l+  | otherwise = error $+    "Statistics.Distribution.Poisson.poisson: lambda must be non-negative. Got "+    ++ show l {-# INLINE poisson #-}  -- $references
Statistics/Distribution/Poisson/Internal.hs view
@@ -14,10 +14,10 @@       probability, poissonEntropy     ) where -import Data.List(unfoldr)+import Data.List (unfoldr) import Numeric.MathFunctions.Constants (m_sqrt_2_pi, m_tiny, m_epsilon) import Numeric.SpecFunctions (logGamma, stirlingError, choose, logFactorial)-import Numeric.SpecFunctions.Extra     (bd0)+import Numeric.SpecFunctions.Extra (bd0)  -- | An unchecked, non-integer-valued version of Loader's saddle point -- algorithm.@@ -50,7 +50,7 @@   where parity j           | even (k-j) = -1           | otherwise  = 1-                         + -- | Returns [x, x^2, x^3, x^4, ...] powers :: Double -> [Double] powers x = unfoldr (\y -> Just (y*x,y*x)) 1@@ -68,7 +68,7 @@ alyThm2 lambda upper lower =   alyThm2Upper lambda upper + 0.5 * (zipCoefficients lambda lower) -zipCoefficients :: Double -> [Double] -> Double +zipCoefficients :: Double -> [Double] -> Double zipCoefficients lambda coefficients =   (sum $ map (uncurry (*)) (zip (powers $ recip lambda) coefficients)) @@ -76,12 +76,12 @@ -- -- poissonMoment[0, s_] := 1 -- poissonMoment[1, s_] := 0--- poissonMoment[k_, s_] := +-- poissonMoment[k_, s_] := --   Sum[s * Binomial[k - 1, j] * poissonMoment[j, s], {j, 0, k - 2}] -- -- upperSeries[m_]  := --  Distribute[Integrate[---    Sum[(-1)^(j - 1) * +--    Sum[(-1)^(j - 1) * --      poissonMoment[j, \[Lambda]] / (j * (j - 1)* \[Lambda]^j), --     {j, 3, 2 m - 1}], --    \[Lambda]]]@@ -89,10 +89,10 @@ -- lowerSeries[m_] := --  Distribute[Integrate[ --    poissonMoment[---      2 m + 2, \[Lambda]] / ((2 m + +--      2 m + 2, \[Lambda]] / ((2 m + --         1)*\[Lambda]^(2 m + 2)), \[Lambda]]] ----- upperBound[m_] := upperSeries[m] + (Log[2*Pi*\[Lambda]] + 1)/2 +-- upperBound[m_] := upperSeries[m] + (Log[2*Pi*\[Lambda]] + 1)/2 -- -- lowerBound[m_] := upperBound[m] + lowerSeries[m] @@ -120,7 +120,7 @@ lowerCoefficients8 = [0,0,0,0,0,0,0, -2027025/8, -15315300, -105252147,                       -178127950, -343908565/4, -10929270, -3721149/14,                       -7709/15, -1/272]-  + upperCoefficients10 :: [Double] upperCoefficients10 = [1/12, 1/24, 19/360, 9,80, 863/2520, 1375/1008,                        33953/5040, 57281/1440, -2271071617/11880,@@ -128,13 +128,13 @@                        -7531072742237/131040, -1405507544003/65520,                        -21001919627/10080, -1365808297/36720,                        -26059/544, -1/5814]-                      + lowerCoefficients10 :: [Double] lowerCoefficients10 = [0,0,0,0,0,0,0,0,0,-130945815/2, -7638505875,                        -438256243425/4, -435477637540, -3552526473925/6,                        -857611717105/3, -545654955967/12, -5794690528/3,                        -578334559/42, -699043/133, -1/420]-                 + upperCoefficients12 :: [Double] upperCoefficients12 = [1/12, 1/24, 19/360, 863/2520, 1375/1008,                        33953/5040, 57281/1440, 3250433/11880,@@ -153,13 +153,13 @@                        -347362037754732, -2205885452434521/100,                        -12237195698286/35, -16926981721/22,                        -6710881/155, -1/600]-                      + -- | Compute entropy directly from its definition. This is just as accurate -- as 'alyThm1' for lambda <= 1 and is faster, but is slow for large lambda, -- and produces some underestimation due to accumulation of floating point -- error. directEntropy :: Double -> Double-directEntropy lambda =   +directEntropy lambda =   negate . sum $   takeWhile (< negate m_epsilon * lambda) $   dropWhile (not . (< negate m_epsilon * lambda)) $
Statistics/Distribution/StudentT.hs view
@@ -23,12 +23,15 @@ import Statistics.Distribution.Transform (LinearTransform (..)) import Numeric.SpecFunctions (   logBeta, incompleteBeta, invIncompleteBeta, digamma)+import Data.Binary (put, get)  -- | Student-T distribution newtype StudentT = StudentT { studentTndf :: Double }                    deriving (Eq, Show, Read, Typeable, Data, Generic) -instance Binary StudentT+instance Binary StudentT where+    put = put . studentTndf+    get = fmap StudentT get  -- | Create Student-T distribution. Number of parameters must be positive. studentT :: Double -> StudentT@@ -76,7 +79,7 @@ instance D.Entropy StudentT where   entropy (StudentT ndf) =     0.5 * (ndf+1) * (digamma ((1+ndf)/2) - digamma(ndf/2))-    + log (sqrt ndf) +    + log (sqrt ndf)     + logBeta (ndf/2) 0.5  instance D.MaybeEntropy StudentT where
Statistics/Distribution/Transform.hs view
@@ -10,16 +10,19 @@ -- Portability : portable -- -- Transformations over distributions-module Statistics.Distribution.Transform (-    LinearTransform (..)-  , linTransFixedPoint-  , scaleAround-  ) where+module Statistics.Distribution.Transform+    (+      LinearTransform (..)+    , linTransFixedPoint+    , scaleAround+    ) where +import Control.Applicative ((<*>)) import Data.Binary (Binary)+import Data.Binary (put, get) import Data.Data (Data, Typeable)+import Data.Functor ((<$>)) import GHC.Generics (Generic)-import Data.Functor          ((<$>)) import qualified Statistics.Distribution as D  -- | Linear transformation applied to distribution.@@ -35,7 +38,9 @@     -- ^ Distribution being transformed.   } deriving (Eq, Show, Read, Typeable, Data, Generic) -instance (Binary d) => Binary (LinearTransform d)+instance (Binary d) => Binary (LinearTransform d) where+    get = LinearTransform <$> get <*> get <*> get+    put (LinearTransform x y z) = put x >> put y >> put z  -- | Apply linear transformation to distribution. scaleAround :: Double           -- ^ Fixed point@@ -73,11 +78,11 @@   variance (LinearTransform _ sc dist) = sc * sc * D.variance dist   stdDev   (LinearTransform _ sc dist) = sc * D.stdDev dist -instance (D.MaybeEntropy d, D.DiscreteDistr d) +instance (D.MaybeEntropy d, D.DiscreteDistr d)          => D.MaybeEntropy (LinearTransform d) where   maybeEntropy (LinearTransform _ _ dist) = D.maybeEntropy dist -instance (D.Entropy d, D.DiscreteDistr d) +instance (D.Entropy d, D.DiscreteDistr d)          => D.Entropy (LinearTransform d) where   entropy (LinearTransform _ _ dist) = D.entropy dist
Statistics/Distribution/Uniform.hs view
@@ -24,6 +24,8 @@ import GHC.Generics (Generic) import qualified Statistics.Distribution as D import qualified System.Random.MWC       as MWC+import Data.Binary (put, get)+import Control.Applicative ((<$>), (<*>))   -- | Uniform distribution from A to B@@ -32,7 +34,9 @@     , uniformB :: {-# UNPACK #-} !Double -- ^ Upper boundary of distribution     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary UniformDistribution+instance Binary UniformDistribution where+    put (UniformDistribution x y) = put x >> put y+    get = UniformDistribution <$> get <*> get  -- | Create uniform distribution. uniformDistr :: Double -> Double -> UniformDistribution
Statistics/Function/Comparison.hs view
@@ -16,9 +16,9 @@       within     ) where -import Control.Monad.ST         (runST)+import Control.Monad.ST (runST)+import Data.Int (Int64) import Data.Primitive.ByteArray (newByteArray, readByteArray, writeByteArray)-import Data.Int                 (Int64)  -- | Compare two 'Double' values for approximate equality, using -- Dawson's method.
Statistics/Math.hs view
@@ -15,7 +15,7 @@ -- 'Numeric.SpecFunctions.Extra' and 'Numeric.Polynomial.Chebyshev'.  module Statistics.Math-{-# DEPRECATED "Use package math-function" #-} +{-# DEPRECATED "Use package math-function" #-}     ( module Numeric.Polynomial.Chebyshev     , module Numeric.SpecFunctions     , module Numeric.SpecFunctions.Extra@@ -24,4 +24,3 @@ import Numeric.Polynomial.Chebyshev import Numeric.SpecFunctions import Numeric.SpecFunctions.Extra-
Statistics/Math/RootFinding.hs view
@@ -20,13 +20,15 @@     -- $references     ) where -import Statistics.Function.Comparison-+import Control.Applicative (Alternative(..), Applicative(..))+import Control.Monad (MonadPlus(..), ap) import Data.Binary (Binary)-import Control.Applicative-import Control.Monad       (MonadPlus(..), ap)+import Data.Binary (put, get)+import Data.Binary.Get (getWord8)+import Data.Binary.Put (putWord8) import Data.Data (Data, Typeable) import GHC.Generics (Generic)+import Statistics.Function.Comparison (within)   -- | The result of searching for a root of a mathematical function.@@ -40,7 +42,18 @@             -- ^ A root was successfully found.               deriving (Eq, Read, Show, Typeable, Data, Generic) -instance (Binary a) => Binary (Root a)+instance (Binary a) => Binary (Root a) where+    put NotBracketed = putWord8 0+    put SearchFailed = putWord8 1+    put (Root a) = putWord8 2 >> put a++    get = do+        i <- getWord8+        case i of+            0 -> return NotBracketed+            1 -> return SearchFailed+            2 -> fmap Root get+            _ -> fail $ "Root.get: Invalid value: " ++ show i  instance Functor Root where     fmap _ NotBracketed = NotBracketed
Statistics/Quantile.hs view
@@ -37,14 +37,14 @@     -- $references     ) where -import Data.Vector.Generic             ((!))+import Data.Vector.Generic ((!)) import Numeric.MathFunctions.Constants (m_epsilon)-import Statistics.Function             (partialSort)+import Statistics.Function (partialSort) import qualified Data.Vector.Generic as G  -- | O(/n/ log /n/). Estimate the /k/th /q/-quantile of a sample, -- using the weighted average method.-weightedAvg :: G.Vector v Double => +weightedAvg :: G.Vector v Double =>                Int        -- ^ /k/, the desired quantile.             -> Int        -- ^ /q/, the number of quantiles.             -> v Double   -- ^ /x/, the sample data.
Statistics/Resampling.hs view
@@ -15,7 +15,12 @@     (       Resample(..)     , jackknife+    , jackknifeMean+    , jackknifeVariance+    , jackknifeVarianceUnb+    , jackknifeStdDev     , resample+    , estimate     ) where  import Control.Concurrent (forkIO, newChan, readChan, writeChan)@@ -29,9 +34,12 @@ import Data.Word (Word32) import GHC.Conc (numCapabilities) import GHC.Generics (Generic)+import Numeric.Sum (Summation(..), kbn) import Statistics.Function (indices)-import Statistics.Types (Estimator, Sample)+import Statistics.Sample (mean, stdDev, variance, varianceUnbiased)+import Statistics.Types (Estimator(..), Sample) import System.Random.MWC (Gen, initialize, uniform, uniformVector)+import qualified Data.Vector.Generic as G import qualified Data.Vector.Unboxed as U import qualified Data.Vector.Unboxed.Mutable as MU @@ -42,7 +50,9 @@       fromResample :: U.Vector Double     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary Resample+instance Binary Resample where+    put = put . fromResample+    get = fmap Resample get  -- | /O(e*r*s)/ Resample a data set repeatedly, with replacement, -- computing each estimate over the resampled data.@@ -80,18 +90,84 @@             forM_ ers $ \(est,arr) ->                 MU.write arr k . est $ re             loop (k+1) ers-      loop start (zip ests results)+      loop start (zip ests' results)   replicateM_ numCapabilities $ readChan done   mapM_ sort results   mapM (liftM Resample . unsafeFreeze) results+ where+  ests' = map estimate ests --- | Compute a statistical estimate repeatedly over a sample, each--- time omitting a successive element.+-- | Run an 'Estimator' over a sample.+estimate :: Estimator -> Sample -> Double+estimate Mean             = mean+estimate Variance         = variance+estimate VarianceUnbiased = varianceUnbiased+estimate StdDev           = stdDev+estimate (Function est) = est++-- | /O(n) or O(n^2)/ Compute a statistical estimate repeatedly over a+-- sample, each time omitting a successive element. jackknife :: Estimator -> Sample -> U.Vector Double-jackknife est sample = U.map f . indices $ sample-    where f i = est (dropAt i sample)-{- INLINE jackknife #-}+jackknife Mean sample             = jackknifeMean sample+jackknife Variance sample         = jackknifeVariance sample+jackknife VarianceUnbiased sample = jackknifeVarianceUnb sample+jackknife StdDev sample = jackknifeStdDev sample+jackknife (Function est) sample+  | G.length sample == 1 = singletonErr "jackknife"+  | otherwise            = U.map f . indices $ sample+  where f i = est (dropAt i sample) +-- | /O(n)/ Compute the jackknife mean of a sample.+jackknifeMean :: Sample -> U.Vector Double+jackknifeMean samp+  | len == 1  = singletonErr "jackknifeMean"+  | otherwise = G.map (/l) $ G.zipWith (+) (pfxSumL samp) (pfxSumR samp)+  where+    l   = fromIntegral (len - 1)+    len = G.length samp++-- | /O(n)/ Compute the jackknife variance of a sample with a+-- correction factor @c@, so we can get either the regular or+-- \"unbiased\" variance.+jackknifeVariance_ :: Double -> Sample -> U.Vector Double+jackknifeVariance_ c samp+  | len == 1  = singletonErr "jackknifeVariance"+  | otherwise = G.zipWith4 go als ars bls brs+  where+    als = pfxSumL . G.map goa $ samp+    ars = pfxSumR . G.map goa $ samp+    goa x = v * v where v = x - m+    bls = pfxSumL . G.map (subtract m) $ samp+    brs = pfxSumR . G.map (subtract m) $ samp+    m = mean samp+    n = fromIntegral len+    go al ar bl br = (al + ar - (b * b) / q) / q+      where b = bl + br+            q = n - (1 + c)+    len = G.length samp++-- | /O(n)/ Compute the unbiased jackknife variance of a sample.+jackknifeVarianceUnb :: Sample -> U.Vector Double+jackknifeVarianceUnb = jackknifeVariance_ 1++-- | /O(n)/ Compute the jackknife variance of a sample.+jackknifeVariance :: Sample -> U.Vector Double+jackknifeVariance = jackknifeVariance_ 0++-- | /O(n)/ Compute the jackknife standard deviation of a sample.+jackknifeStdDev :: Sample -> U.Vector Double+jackknifeStdDev = G.map sqrt . jackknifeVarianceUnb++pfxSumL :: U.Vector Double -> U.Vector Double+pfxSumL = G.map kbn . G.scanl add zero++pfxSumR :: U.Vector Double -> U.Vector Double+pfxSumR = G.tail . G.map kbn . G.scanr (flip add) zero+ -- | Drop the /k/th element of a vector. dropAt :: U.Unbox e => Int -> U.Vector e -> U.Vector e dropAt n v = U.slice 0 n v U.++ U.slice (n+1) (U.length v - n - 1) v++singletonErr :: String -> a+singletonErr func = error $+                    "Statistics.Resampling." ++ func ++ ": singleton input"
Statistics/Resampling/Bootstrap.hs view
@@ -21,20 +21,23 @@     -- $references     ) where +import Control.Applicative ((<$>), (<*>)) import Control.DeepSeq (NFData) import Control.Exception (assert)-import Control.Monad.Par               (parMap,runPar)+import Control.Monad.Par (parMap, runPar) import Data.Binary (Binary)+import Data.Binary (put, get) import Data.Data (Data) import Data.Typeable (Typeable) import Data.Vector.Unboxed ((!))-import GHC.Generics+import GHC.Generics (Generic) import Statistics.Distribution (cumulative, quantile) import Statistics.Distribution.Normal import Statistics.Resampling (Resample(..), jackknife) import Statistics.Sample (mean) import Statistics.Types (Estimator, Sample) import qualified Data.Vector.Unboxed as U+import qualified Statistics.Resampling as R  -- | A point and interval estimate computed via an 'Estimator'. data Estimate = Estimate {@@ -50,7 +53,9 @@     -- ^ Confidence level of the confidence intervals.     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary Estimate+instance Binary Estimate where+    put (Estimate w x y z) = put w >> put x >> put y >> put z+    get = Estimate <$> get <*> get <*> get <*> get instance NFData Estimate  -- | Multiply the point, lower bound, and upper bound in an 'Estimate'@@ -93,7 +98,7 @@       | otherwise =           estimate pt (resample ! lo) (resample ! hi) confidenceLevel       where-        pt    = est sample+        pt    = R.estimate est sample         lo    = max (cumn a1) 0           where a1 = bias + b1 / (1 - accel * b1)                 b1 = bias + z1
Statistics/Sample.hs view
@@ -21,6 +21,7 @@      -- * Statistics of location     , mean+    , welfordMean     , meanWeighted     , harmonicMean     , geometricMean@@ -54,11 +55,14 @@     ) where  import Statistics.Function (minMax)+import Statistics.Sample.Internal (robustSumVar, sum) import Statistics.Types (Sample,WeightedSample)+import qualified Data.Vector as V import qualified Data.Vector.Generic as G+import qualified Data.Vector.Unboxed as U  -- Operator ^ will be overriden-import Prelude hiding ((^))+import Prelude hiding ((^), sum)  -- | /O(n)/ Range. The difference between the largest and smallest -- elements of a sample.@@ -67,19 +71,31 @@     where (lo , hi) = minMax s {-# INLINE range #-} +-- | /O(n)/ Arithmetic mean.  This uses Kahan-Babuška-Neumaier+-- summation, so is more accurate than 'welfordMean' unless the input+-- values are very large.+mean :: (G.Vector v Double) => v Double -> Double+mean xs = sum xs / fromIntegral (G.length xs)+{-# SPECIALIZE mean :: U.Vector Double -> Double #-}+{-# SPECIALIZE mean :: V.Vector Double -> Double #-}+ -- | /O(n)/ Arithmetic mean.  This uses Welford's algorithm to provide -- numerical stability, using a single pass over the sample data.-mean :: (G.Vector v Double) => v Double -> Double-mean = fini . G.foldl' go (T 0 0)+--+-- Compared to 'mean', this loses a surprising amount of precision+-- unless the inputs are very large.+welfordMean :: (G.Vector v Double) => v Double -> Double+welfordMean = fini . G.foldl' go (T 0 0)   where     fini (T a _) = a     go (T m n) x = T m' n'         where m' = m + (x - m) / fromIntegral n'               n' = n + 1-{-# INLINE mean #-}+{-# SPECIALIZE welfordMean :: U.Vector Double -> Double #-}+{-# SPECIALIZE welfordMean :: V.Vector Double -> Double #-}  -- | /O(n)/ Arithmetic mean for weighted sample. It uses a single-pass--- algorithm analogous to the one used by 'mean'.+-- algorithm analogous to the one used by 'welfordMean'. meanWeighted :: (G.Vector v (Double,Double)) => v (Double,Double) -> Double meanWeighted = fini . G.foldl' go (V 0 0)     where@@ -117,7 +133,7 @@     | a < 0  = error "Statistics.Sample.centralMoment: negative input"     | a == 0 = 1     | a == 1 = 0-    | otherwise = G.sum (G.map go xs) / fromIntegral (G.length xs)+    | otherwise = sum (G.map go xs) / fromIntegral (G.length xs)   where     go x = (x-m) ^ a     m    = mean xs@@ -202,11 +218,6 @@  data V = V {-# UNPACK #-} !Double {-# UNPACK #-} !Double -robustSumVar :: (G.Vector v Double) => Double -> v Double -> Double-robustSumVar m = G.sum . G.map (square . subtract m)-  where square x = x * x-{-# INLINE robustSumVar #-}- -- | Maximum likelihood estimate of a sample's variance.  Also known -- as the population variance, where the denominator is /n/. variance :: (G.Vector v Double) => v Double -> Double@@ -242,7 +253,7 @@ -- | Calculate mean and unbiased estimate of variance. This -- function should be used if both mean and variance are required -- since it will calculate mean only once.-meanVarianceUnb ::  (G.Vector v Double) => v Double -> (Double,Double)+meanVarianceUnb :: (G.Vector v Double) => v Double -> (Double,Double) meanVarianceUnb samp   | n > 1     = (m, robustSumVar m samp / fromIntegral (n-1))   | otherwise = (m, 0)
+ Statistics/Sample/Internal.hs view
@@ -0,0 +1,30 @@+{-# LANGUAGE FlexibleContexts #-}++-- |+-- Module    : Statistics.Sample.Internal+-- Copyright : (c) 2013 Bryan O'Sullivan+-- License   : BSD3+--+-- Maintainer  : bos@serpentine.com+-- Stability   : experimental+-- Portability : portable+--+-- Internal functions for computing over samples.+module Statistics.Sample.Internal+    (+      robustSumVar+    , sum+    ) where++import Numeric.Sum (kbn, sumVector)+import Prelude hiding (sum)+import qualified Data.Vector.Generic as G++robustSumVar :: (G.Vector v Double) => Double -> v Double -> Double+robustSumVar m = sum . G.map (square . subtract m)+  where square x = x * x+{-# INLINE robustSumVar #-}++sum :: (G.Vector v Double) => v Double -> Double+sum = sumVector kbn+{-# INLINE sum #-}
Statistics/Sample/KernelDensity.hs view
@@ -25,17 +25,17 @@     -- $references     ) where -import Prelude hiding (const,min,max) import Numeric.MathFunctions.Constants (m_sqrt_2_pi)-import Statistics.Function             (minMax, nextHighestPowerOfTwo)-import Statistics.Math.RootFinding     (fromRoot, ridders)-import Statistics.Sample.Histogram     (histogram_)-import Statistics.Transform            (dct, idct)+import Prelude hiding (const, min, max, sum)+import Statistics.Function (minMax, nextHighestPowerOfTwo)+import Statistics.Math.RootFinding (fromRoot, ridders)+import Statistics.Sample.Histogram (histogram_)+import Statistics.Sample.Internal (sum)+import Statistics.Transform (dct, idct) import qualified Data.Vector.Generic as G import qualified Data.Vector.Unboxed as U  - -- | Gaussian kernel density estimator for one-dimensional data, using -- the method of Botev et al. --@@ -87,13 +87,13 @@     !n  = fromIntegral ni     !ni = nextHighestPowerOfTwo n0     !r  = max - min-    a   = dct . G.map (/ G.sum h) $ h+    a   = dct . G.map (/ sum h) $ h         where h = G.map (/ len) $ histogram_ ni min max xs     !len    = fromIntegral (G.length xs)     !t_star = fromRoot (0.28 * len ** (-0.4)) . ridders 1e-14 (0,0.1) $ \x ->               x - (len * (2 * sqrt pi) * go 6 (f 7 x)) ** (-0.4)       where-        f q t = 2 * pi ** (q*2) * G.sum (G.zipWith g iv a2v)+        f q t = 2 * pi ** (q*2) * sum (G.zipWith g iv a2v)           where g i a2 = i ** q * a2 * exp ((-i) * sqr pi * t)                 a2v = G.map (sqr . (*0.5)) $ G.tail a                 iv = G.map sqr $ G.enumFromTo 1 (n-1)
Statistics/Sample/KernelDensity/Simple.hs view
@@ -51,17 +51,21 @@ import Data.Vector.Binary () import GHC.Generics (Generic) import Numeric.MathFunctions.Constants (m_1_sqrt_2, m_2_sqrt_pi)+import Prelude hiding (sum) import Statistics.Function (minMax)-import Statistics.Sample   (stdDev)-import qualified Data.Vector.Unboxed as U+import Statistics.Sample (stdDev)+import Statistics.Sample.Internal (sum) import qualified Data.Vector.Generic as G+import qualified Data.Vector.Unboxed as U  -- | Points from the range of a 'Sample'. newtype Points = Points {       fromPoints :: U.Vector Double     } deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary Points+instance Binary Points where+    get = fmap Points get+    put = put . fromPoints  -- | Bandwidth estimator for an Epanechnikov kernel. epanechnikovBW :: Double -> Bandwidth@@ -148,7 +152,7 @@     | n < 2     = errorShort "estimatePDF"     | otherwise = U.map k . fromPoints   where-    k p = G.sum . G.map (kernel f h p) $ sample+    k p = sum . G.map (kernel f h p) $ sample     f   = 1 / (h * fromIntegral n)     n   = G.length sample {-# INLINE estimatePDF #-}
Statistics/Sample/Powers.hs view
@@ -50,22 +50,25 @@ import Data.Binary (Binary(..)) import Data.Data (Data, Typeable) import Data.Vector.Binary ()-import Data.Vector.Generic   (unsafeFreeze)-import Data.Vector.Unboxed   ((!))+import Data.Vector.Generic (unsafeFreeze)+import Data.Vector.Unboxed ((!)) import GHC.Generics (Generic)-import Prelude hiding (sum)-import Statistics.Function   (indexed)-import Statistics.Internal   (inlinePerformIO) import Numeric.SpecFunctions (choose)-import System.IO.Unsafe      (unsafePerformIO)-import qualified Data.Vector.Unboxed as U+import Prelude hiding (sum)+import Statistics.Function (indexed)+import Statistics.Internal (inlinePerformIO)+import System.IO.Unsafe (unsafePerformIO) import qualified Data.Vector.Generic as G+import qualified Data.Vector.Unboxed as U import qualified Data.Vector.Unboxed.Mutable as MU+import qualified Statistics.Sample.Internal as S  newtype Powers = Powers (U.Vector Double)     deriving (Eq, Read, Show, Typeable, Data, Generic) -instance Binary Powers+instance Binary Powers where+    put (Powers v) = put v+    get = fmap Powers get  -- | O(/n/) Collect the /n/ simple powers of a sample. --@@ -112,7 +115,7 @@                   error ("Statistics.Sample.Powers.centralMoment: "                          ++ "invalid argument")     | k == 0    = 1-    | otherwise = (/n) . U.sum . U.map go . indexed . U.take (k+1) $ pa+    | otherwise = (/n) . S.sum . U.map go . indexed . U.take (k+1) $ pa   where     go (i , e) = (k `choose` i) * ((-m) ^ (k-i)) * e     n = U.head pa
Statistics/Test/ChiSquared.hs view
@@ -7,11 +7,12 @@   , TestResult(..)   ) where -import qualified Data.Vector.Generic as G-+import Prelude hiding (sum) import Statistics.Distribution import Statistics.Distribution.ChiSquared+import Statistics.Sample.Internal (sum) import Statistics.Test.Types+import qualified Data.Vector.Generic as G   -- | Generic form of Pearson chi squared tests for binned data. Data@@ -33,7 +34,7 @@   | otherwise      = error $ "Statistics.Test.ChiSquare.chi2test: bad p-value: " ++ show p   where     n     = G.length vec - ndf - 1-    chi2  = G.sum $ G.map (\(o,e) -> sqr (fromIntegral o - e) / e) vec+    chi2  = sum $ G.map (\(o,e) -> sqr (fromIntegral o - e) / e) vec     d     = chiSquared n     sqr x = x * x {-# INLINE chi2test #-}
Statistics/Test/KolmogorovSmirnov.hs view
@@ -29,21 +29,19 @@     -- $references   ) where -import Control.Monad-import Control.Monad.ST  (ST)--import qualified Data.Vector.Unboxed         as U+import Control.Monad (when)+import Control.Monad.ST (ST)+import Prelude hiding (sum)+import Statistics.Distribution (Distribution(..))+import Statistics.Function (sort)+import Statistics.Sample.Internal (sum)+import Statistics.Test.Types (TestResult(..), TestType(..), significant)+import Statistics.Types (Sample)+import Text.Printf (printf)+import qualified Data.Vector.Unboxed as U import qualified Data.Vector.Unboxed.Mutable as M -import Statistics.Distribution        (Distribution(..))-import Statistics.Types               (Sample)-import Statistics.Function            (sort)-import Statistics.Test.Types -import Text.Printf--- ---------------------------------------------------------------- -- Test ----------------------------------------------------------------@@ -267,7 +265,7 @@ matrixMultiply (Matrix n xs e1) (Matrix _ ys e2) =   Matrix n (U.generate (n*n) go) (e1 + e2)   where-    go i = U.sum $ U.zipWith (*) row col+    go i = sum $ U.zipWith (*) row col       where         nCol = i `rem` n         row  = U.slice (i - nCol) n xs
Statistics/Test/MannWhitneyU.hs view
@@ -27,20 +27,18 @@   ) where  import Control.Applicative ((<$>))-import Data.List           (findIndex)-import Data.Ord            (comparing)-import qualified Data.Vector.Unboxed as U--import Numeric.SpecFunctions          (choose)--import Statistics.Distribution        (quantile)+import Data.List (findIndex)+import Data.Ord (comparing)+import Numeric.SpecFunctions (choose)+import Prelude hiding (sum)+import Statistics.Distribution (quantile) import Statistics.Distribution.Normal (standard)-import Statistics.Types               (Sample)-import Statistics.Function            (sortBy)-import Statistics.Test.Types-import Statistics.Test.Internal--+import Statistics.Function (sortBy)+import Statistics.Sample.Internal (sum)+import Statistics.Test.Internal (rank, splitByTags)+import Statistics.Test.Types (TestResult(..), TestType(..), significant)+import Statistics.Types (Sample)+import qualified Data.Vector.Unboxed as U  -- | The Wilcoxon Rank Sums Test. --@@ -54,8 +52,7 @@ -- and the related functions for testing significance, but this function is exposed -- for completeness. wilcoxonRankSums :: Sample -> Sample -> (Double, Double)-wilcoxonRankSums xs1 xs2 = ( U.sum ranks1 , U.sum ranks2-                           )+wilcoxonRankSums xs1 xs2 = (sum ranks1, sum ranks2)   where     -- Ranks for each sample     (ranks1,ranks2) = splitByTags $ U.zip tags (rank (==) joinSample)@@ -138,12 +135,12 @@     n = bigN - m -} --- Memoised version of the original a function, above. +-- Memoised version of the original a function, above. -- -- Doubles are stored to avoid integer overflow. 32-bit Ints begin to -- overflow for bigN as small as 33 (64-bit one at 66) while Double to -- go to infinity till bigN=1029--- +-- -- -- outer list is indexed by big N - 2 -- inner list by (m-1) (we know m < bigN)
Statistics/Test/WilcoxonT.hs view
@@ -25,34 +25,34 @@   , TestResult(..)   ) where -import Control.Applicative ((<$>))-import Data.Function       (on)-import Data.List           (findIndex)-import Data.Ord            (comparing)-import qualified Data.Vector.Unboxed as U -import Statistics.Types               (Sample)-import Statistics.Function            (sortBy)-import Statistics.Test.Types-import Statistics.Test.Internal ---- | The Wilcoxon matched-pairs signed-rank test. --+--+--+-- Note that: wilcoxonMatchedPairSignedRank == (\(x, y) -> (y, x)) . flip wilcoxonMatchedPairSignedRank+-- The samples are zipped together: if one is longer than the other, both are truncated -- The value returned is the pair (T+, T-).  T+ is the sum of positive ranks (the--- ranks of the differences where the first parameter is higher) whereas T- is--- the sum of negative ranks (the ranks of the differences where the second parameter is higher). -- These values mean little by themselves, and should be combined with the 'wilcoxonSignificant' -- function in this module to get a meaningful result.------ The samples are zipped together: if one is longer than the other, both are truncated+-- ranks of the differences where the first parameter is higher) whereas T- is+-- the sum of negative ranks (the ranks of the differences where the second parameter is higher). -- to the the length of the shorter sample.------ Note that: wilcoxonMatchedPairSignedRank == (\(x, y) -> (y, x)) . flip wilcoxonMatchedPairSignedRank++import Control.Applicative ((<$>))+import Data.Function (on)+import Data.List (findIndex)+import Data.Ord (comparing)+import Prelude hiding (sum)+import Statistics.Function (sortBy)+import Statistics.Sample.Internal (sum)+import Statistics.Test.Internal (rank, splitByTags)+import Statistics.Test.Types (TestResult(..), TestType(..), significant)+import Statistics.Types (Sample)+import qualified Data.Vector.Unboxed as U+ wilcoxonMatchedPairSignedRank :: Sample -> Sample -> (Double, Double)-wilcoxonMatchedPairSignedRank a b = (          U.sum ranks1-                                    , negate $ U.sum ranks2-                                    )+wilcoxonMatchedPairSignedRank a b = (sum ranks1, negate (sum ranks2))   where     (ranks1, ranks2) = splitByTags                      $ U.zip tags (rank ((==) `on` abs) diffs)
Statistics/Transform.hs view
@@ -29,14 +29,14 @@     , ifft     ) where -import Control.Monad         (when)-import Control.Monad.ST      (ST)-import Data.Bits             (shiftL, shiftR)-import Data.Complex          (Complex(..), conjugate, realPart)+import Control.Monad (when)+import Control.Monad.ST (ST)+import Data.Bits (shiftL, shiftR)+import Data.Complex (Complex(..), conjugate, realPart) import Numeric.SpecFunctions (log2)-import qualified Data.Vector.Generic         as G+import qualified Data.Vector.Generic as G import qualified Data.Vector.Generic.Mutable as M-import qualified Data.Vector.Unboxed         as U+import qualified Data.Vector.Unboxed as U   type CD = Complex Double@@ -90,7 +90,7 @@     interleave z | even z    = vals `G.unsafeIndex` halve z                  | otherwise = vals `G.unsafeIndex` (len - halve z - 1)     vals = G.map realPart . ifft $ G.zipWith (*) weights xs-    weights +    weights       = G.cons n       $ G.generate (len - 1) $ \x -> 2 * n * exp ((0:+1) * fi (x+1) * pi/(2*n))       where n = fi len
Statistics/Types.hs view
@@ -11,7 +11,7 @@  module Statistics.Types     (-      Estimator+      Estimator(..)     , Sample     , WeightedSample     , Weights@@ -25,9 +25,16 @@ -- | Sample with weights. First element of sample is data, second is weight type WeightedSample = U.Vector (Double,Double) --- | A function that estimates a property of a sample, such as its--- 'mean'.-type Estimator = Sample -> Double+-- | An estimator of a property of a sample, such as its 'mean'.+--+-- The use of an algebraic data type here allows functions such as+-- 'jackknife' and 'bootstrapBCA' to use more efficient algorithms+-- when possible.+data Estimator = Mean+               | Variance+               | VarianceUnbiased+               | StdDev+               | Function (Sample -> Double)  -- | Weights for affecting the importance of elements of a sample. type Weights = U.Vector Double
benchmark/bench.hs view
@@ -1,12 +1,10 @@ import Control.Monad.ST (runST)-import Data.Complex-import qualified Data.Vector.Unboxed as U--import System.Random.MWC import Criterion.Main-+import Data.Complex import Statistics.Sample import Statistics.Transform+import System.Random.MWC+import qualified Data.Vector.Unboxed as U   -- Test sample
statistics.cabal view
@@ -1,5 +1,5 @@ name:           statistics-version:        0.10.5.2+version:        0.11.0.0 synopsis:       A library of statistical types, data, and functions description:   This library provides a number of common functions and types useful@@ -87,15 +87,16 @@     Statistics.Distribution.Poisson.Internal     Statistics.Function.Comparison     Statistics.Internal+    Statistics.Sample.Internal     Statistics.Test.Internal   build-depends:     base < 5,-    binary >= 0.6.3.0,+    binary >= 0.5.1.0,     deepseq >= 1.1.0.2,     erf,     monad-par         >= 0.3.4,     mwc-random        >= 0.13.0.0,-    math-functions    >= 0.1.2,+    math-functions    >= 0.1.5.2,     primitive         >= 0.3,     vector            >= 0.7.1,     vector-algorithms >= 0.4,@@ -122,8 +123,8 @@     Tests.Distribution     Tests.Helpers     Tests.Function-    Tests.NonparametricTest-    Tests.NonparametricTest.Table+    Tests.NonParametric+    Tests.NonParametric.Table     Tests.Transform     Tests.KDE @@ -132,6 +133,7 @@    build-depends:     base,+    binary,     ieee754 >= 0.7.3,     HUnit,     QuickCheck >= 2,
tests/Tests/Distribution.hs view
@@ -1,51 +1,41 @@ {-# OPTIONS_GHC -fno-warn-orphans #-}-{-# LANGUAGE ScopedTypeVariables  #-}--- Required for Param-{-# LANGUAGE FlexibleInstances    #-}-{-# LANGUAGE OverlappingInstances #-}-{-# LANGUAGE ViewPatterns #-}-module Tests.Distribution (-    distributionTests-  ) where--import Control.Applicative-import Control.Exception+{-# LANGUAGE FlexibleInstances, OverlappingInstances, ScopedTypeVariables,+    ViewPatterns #-}+module Tests.Distribution (tests) where -import Data.List     (find)+import Control.Applicative ((<$>), (<*>))+import Data.Binary (Binary, decode, encode)+import Data.List (find) import Data.Typeable (Typeable)--import qualified Numeric.IEEE    as IEEE--import Test.Framework                       (Test,testGroup)-import Test.Framework.Providers.QuickCheck2 (testProperty)-import Test.QuickCheck         as QC-import Test.QuickCheck.Monadic as QC-import Text.Printf- import Statistics.Distribution-import Statistics.Distribution.Beta-import Statistics.Distribution.Binomial-import Statistics.Distribution.ChiSquared+import Statistics.Distribution.Beta (BetaDistribution, betaDistr)+import Statistics.Distribution.Binomial (BinomialDistribution, binomial) import Statistics.Distribution.CauchyLorentz-import Statistics.Distribution.Exponential-import Statistics.Distribution.FDistribution-import Statistics.Distribution.Gamma+import Statistics.Distribution.ChiSquared (ChiSquared, chiSquared)+import Statistics.Distribution.Exponential (ExponentialDistribution, exponential)+import Statistics.Distribution.FDistribution (FDistribution, fDistribution)+import Statistics.Distribution.Gamma (GammaDistribution, gammaDistr) import Statistics.Distribution.Geometric import Statistics.Distribution.Hypergeometric-import Statistics.Distribution.Normal-import Statistics.Distribution.Poisson+import Statistics.Distribution.Normal (NormalDistribution, normalDistr)+import Statistics.Distribution.Poisson (PoissonDistribution, poisson) import Statistics.Distribution.StudentT-import Statistics.Distribution.Transform-import Statistics.Distribution.Uniform--import Prelude hiding (catch)--import Tests.Helpers+import Statistics.Distribution.Transform (LinearTransform, linTransDistr)+import Statistics.Distribution.Uniform (UniformDistribution, uniformDistr)+import Test.Framework (Test, testGroup)+import Test.Framework.Providers.QuickCheck2 (testProperty)+import Test.QuickCheck as QC+import Test.QuickCheck.Monadic as QC+import Tests.Helpers (T(..), (=~), eq, testAssertion, typeName)+import Tests.Helpers (monotonicallyIncreasesIEEE)+import Text.Printf (printf)+import qualified Control.Exception as E+import qualified Numeric.IEEE as IEEE   -- | Tests for all distributions-distributionTests :: Test-distributionTests = testGroup "Tests for all distributions"+tests :: Test+tests = testGroup "Tests for all distributions"   [ contDistrTests (T :: T BetaDistribution        )   , contDistrTests (T :: T CauchyDistribution      )   , contDistrTests (T :: T ChiSquared              )@@ -71,7 +61,7 @@ ----------------------------------------------------------------  -- Tests for continous distribution-contDistrTests :: (Param d, ContDistr d, QC.Arbitrary d, Typeable d, Show d) => T d -> Test+contDistrTests :: (Param d, ContDistr d, QC.Arbitrary d, Typeable d, Show d, Binary d, Eq d) => T d -> Test contDistrTests t = testGroup ("Tests for: " ++ typeName t) $   cdfTests t ++   [ testProperty "PDF sanity"              $ pdfSanityCheck     t@@ -81,7 +71,7 @@   ]  -- Tests for discrete distribution-discreteDistrTests :: (Param d, DiscreteDistr d, QC.Arbitrary d, Typeable d, Show d) => T d -> Test+discreteDistrTests :: (Param d, DiscreteDistr d, QC.Arbitrary d, Typeable d, Show d, Binary d, Eq d) => T d -> Test discreteDistrTests t = testGroup ("Tests for: " ++ typeName t) $   cdfTests t ++   [ testProperty "Prob. sanity"         $ probSanityCheck       t@@ -91,7 +81,7 @@   ]  -- Tests for distributions which have CDF-cdfTests :: (Param d, Distribution d, QC.Arbitrary d, Show d) => T d -> [Test]+cdfTests :: (Param d, Distribution d, QC.Arbitrary d, Show d, Binary d, Eq d) => T d -> [Test] cdfTests t =   [ testProperty "C.D.F. sanity"        $ cdfSanityCheck         t   , testProperty "CDF limit at +inf"    $ cdfLimitAtPosInfinity  t@@ -100,12 +90,15 @@   , testProperty "CDF at -inf = 1"      $ cdfAtNegInfinity       t   , testProperty "CDF is nondecreasing" $ cdfIsNondecreasing     t   , testProperty "1-CDF is correct"     $ cdfComplementIsCorrect t+  , testProperty "Binary OK"            $ p_binary t   ]++ ----------------------------------------------------------------  -- CDF is in [0,1] range cdfSanityCheck :: (Distribution d) => T d -> d -> Double -> Bool-cdfSanityCheck _ d x = c >= 0 && c <= 1 +cdfSanityCheck _ d x = c >= 0 && c <= 1   where c = cumulative d x  -- CDF never decreases@@ -148,7 +141,7 @@ cdfDiscreteIsCorrect :: (DiscreteDistr d) => T d -> d -> Property cdfDiscreteIsCorrect _ d   = printTestCase (unlines badN)-  $ null badN  +  $ null badN   where     -- We are checking that:     --@@ -202,15 +195,15 @@ -- Test that quantile fails if p<0 or p>1 quantileShouldFail :: (ContDistr d) => T d -> d -> Double -> Property quantileShouldFail _ d p =-  p < 0 || p > 1 ==> QC.monadicIO $ do r <- QC.run $ catch+  p < 0 || p > 1 ==> QC.monadicIO $ do r <- QC.run $ E.catch                                               (do { return $! quantile d p; return False })-                                              (\(e :: SomeException) -> return True)+                                              (\(_ :: E.SomeException) -> return True)                                        QC.assert r   -- Probability is in [0,1] range probSanityCheck :: (DiscreteDistr d) => T d -> d -> Int -> Bool-probSanityCheck _ d x = p >= 0 && p <= 1 +probSanityCheck _ d x = p >= 0 && p <= 1   where p = probability d x  -- Check that discrete CDF is correct@@ -245,7 +238,11 @@     logP = logProbability d x  -    +p_binary :: (Eq a, Show a, Binary a) => T a -> a -> Bool+p_binary _ a = a == (decode . encode) a+++ ---------------------------------------------------------------- -- Arbitrary instances for ditributions ----------------------------------------------------------------@@ -289,7 +286,7 @@            <*> ((abs <$> arbitrary))            <*> ((abs <$> arbitrary) `suchThat` (>0)) instance QC.Arbitrary FDistribution where-  arbitrary =  fDistribution +  arbitrary =  fDistribution            <$> ((abs <$> arbitrary) `suchThat` (>0))            <*> ((abs <$> arbitrary) `suchThat` (>0))
tests/Tests/Function.hs view
@@ -1,15 +1,11 @@ module Tests.Function ( tests ) where -import qualified Data.Vector.Unboxed as U-import           Data.Vector.Unboxed   ((!))--import Test.QuickCheck+import Statistics.Function import Test.Framework import Test.Framework.Providers.QuickCheck2-+import Test.QuickCheck import Tests.Helpers-import Statistics.Function-+import qualified Data.Vector.Unboxed as U   tests :: Test@@ -29,5 +25,5 @@ p_nextHighestPowerOfTwo   = all (\(good, is) -> all ((==good) . nextHighestPowerOfTwo) is) lists   where-    pows  = [1 .. 17]+    pows  = [1 .. 17 :: Int]     lists = [ (2^m, [2^n+1 .. 2^m]) | (n,m) <- pows `zip` tail pows ]
tests/Tests/KDE.hs view
@@ -1,18 +1,16 @@ -- | Tests for Kernel density estimates.-module Tests.KDE ( -  tests +module Tests.KDE (+  tests   )where  import Data.Vector.Unboxed ((!))-import qualified Data.Vector.Unboxed as U--import Test.Framework                       (Test, testGroup)-import Test.Framework.Providers.QuickCheck2 (testProperty)-import Test.QuickCheck                      -import Text.Printf-+import Numeric.Sum (kbn, sumVector) import Statistics.Sample.KernelDensity-+import Test.Framework (Test, testGroup)+import Test.Framework.Providers.QuickCheck2 (testProperty)+import Test.QuickCheck (Property, (==>), printTestCase)+import Text.Printf (printf)+import qualified Data.Vector.Unboxed as U   tests :: Test@@ -21,7 +19,7 @@   ]  t_densityIsPDF :: [Double] -> Property-t_densityIsPDF vec +t_densityIsPDF vec   = not (null vec) ==> test   where     (xs,ys)  = kde 4096 (U.fromList vec)@@ -31,11 +29,11 @@     test = printTestCase (printf "Integral %f" integral)          $ abs (1 - integral) <= 1e-3 -           + integratePDF :: Double -> U.Vector Double -> Double-integratePDF step vec -  = step * U.sum (U.zipWith (*) vec weights)+integratePDF step vec+  = step * sumVector kbn (U.zipWith (*) vec weights)   where     n       = U.length vec     weights = U.generate n go
+ tests/Tests/NonParametric.hs view
@@ -0,0 +1,226 @@+-- Tests for Statistics.Test.NonParametric+module Tests.NonParametric (tests) where++import Statistics.Distribution.Normal (standard)+import Statistics.Test.KolmogorovSmirnov+import Statistics.Test.MannWhitneyU+import Statistics.Test.WilcoxonT+import Test.Framework (Test, testGroup)+import Test.Framework.Providers.HUnit+import Test.HUnit (assertEqual)+import Tests.Helpers (eq, testAssertion, testEquality)+import Tests.NonParametric.Table (tableKSD, tableKS2D)+import qualified Data.Vector.Unboxed as U+++tests :: Test+tests = testGroup "Nonparametric tests"+        $ concat [ mannWhitneyTests+                 , wilcoxonSumTests+                 , wilcoxonPairTests+                 , kolmogorovSmirnovDTest+                 ]++----------------------------------------------------------------++mannWhitneyTests :: [Test]+mannWhitneyTests = zipWith test [(0::Int)..] testData +++  [ testEquality "Mann-Whitney U Critical Values, m=1"+      (replicate (20*3) Nothing)+      [mannWhitneyUCriticalValue (1,x) p | x <- [1..20], p <- [0.005,0.01,0.025]]+  , testEquality "Mann-Whitney U Critical Values, m=2, p=0.025"+      (replicate 7 Nothing ++ map Just [0,0,0,0,1,1,1,1,1,2,2,2,2])+      [mannWhitneyUCriticalValue (2,x) 0.025 | x <- [1..20]]+  , testEquality "Mann-Whitney U Critical Values, m=6, p=0.05"+      (replicate 1 Nothing ++ map Just [0, 2,3,5,7,8,10,12,14,16,17,19,21,23,25,26,28,30,32])+      [mannWhitneyUCriticalValue (6,x) 0.05 | x <- [1..20]]+  , testEquality "Mann-Whitney U Critical Values, m=20, p=0.025"+      (replicate 1 Nothing ++ map Just [2,8,14,20,27,34,41,48,55,62,69,76,83,90,98,105,112,119,127])+      [mannWhitneyUCriticalValue (20,x) 0.025 | x <- [1..20]]+  ]+  where+    test n (a, b, c, d)+      = testCase "Mann-Whitney" $ do+          assertEqual ("Mann-Whitney U "     ++ show n) c us+          assertEqual ("Mann-Whitney U Sig " ++ show n) d ss+      where+        us = mannWhitneyU (U.fromList a) (U.fromList b)+        ss = mannWhitneyUSignificant TwoTailed (length a, length b) 0.05 us+    -- List of (Sample A, Sample B, (Positive Rank, Negative Rank))+    testData :: [([Double], [Double], (Double, Double), Maybe TestResult)]+    testData = [ ( [3,4,2,6,2,5]+                 , [9,7,5,10,6,8]+                 , (2, 34)+                 , Just Significant+                 )+               , ( [540,480,600,590,605]+                 , [760,890,1105,595,940]+                 , (2, 23)+                 , Just Significant+                 )+               , ( [19,22,16,29,24]+                 , [20,11,17,12]+                 , (17, 3)+                 , Just NotSignificant+                 )+               , ( [126,148,85,61, 179,93, 45,189,85,93]+                 , [194,128,69,135,171,149,89,248,79,137]+                 , (35,65)+                 , Just NotSignificant+                 )+               , ( [1..30]+                 , [1..30]+                 , (450,450)+                 , Just NotSignificant+                 )+               , ( [1 .. 30]+                 , [11.5 .. 40 ]+                 , (190.0,710.0)+                 , Just Significant+                 )+               ]++wilcoxonSumTests :: [Test]+wilcoxonSumTests = zipWith test [(0::Int)..] testData+  where+    test n (a, b, c) = testCase "Wilcoxon Sum"+                     $ assertEqual ("Wilcoxon Sum " ++ show n) c (wilcoxonRankSums (U.fromList a) (U.fromList b))+    -- List of (Sample A, Sample B, (Positive Rank, Negative Rank))+    testData :: [([Double], [Double], (Double, Double))]+    testData = [ ( [8.50,9.48,8.65,8.16,8.83,7.76,8.63]+                 , [8.27,8.20,8.25,8.14,9.00,8.10,7.20,8.32,7.70]+                 , (75, 61)+                 )+               , ( [0.45,0.50,0.61,0.63,0.75,0.85,0.93]+                 , [0.44,0.45,0.52,0.53,0.56,0.58,0.58,0.65,0.79]+                 , (71.5, 64.5)+                 )+               ]++wilcoxonPairTests :: [Test]+wilcoxonPairTests = zipWith test [(0::Int)..] testData +++  -- Taken from the Mitic paper:+  [ testAssertion "Sig 16, 35" (to4dp 0.0467 $ wilcoxonMatchedPairSignificance 16 35)+  , testAssertion "Sig 16, 36" (to4dp 0.0523 $ wilcoxonMatchedPairSignificance 16 36)+  , testEquality   "Wilcoxon critical values, p=0.05"+      (replicate 4 Nothing ++ map Just [0,2,3,5,8,10,13,17,21,25,30,35,41,47,53,60,67,75,83,91,100,110,119])+      [wilcoxonMatchedPairCriticalValue x 0.05 | x <- [1..27]]+  , testEquality "Wilcoxon critical values, p=0.025"+      (replicate 5 Nothing ++ map Just [0,2,3,5,8,10,13,17,21,25,29,34,40,46,52,58,65,73,81,89,98,107])+      [wilcoxonMatchedPairCriticalValue x 0.025 | x <- [1..27]]+  , testEquality "Wilcoxon critical values, p=0.01"+      (replicate 6 Nothing ++ map Just [0,1,3,5,7,9,12,15,19,23,27,32,37,43,49,55,62,69,76,84,92])+      [wilcoxonMatchedPairCriticalValue x 0.01 | x <- [1..27]]+  , testEquality "Wilcoxon critical values, p=0.005"+      (replicate 7 Nothing ++ map Just [0,1,3,5,7,9,12,15,19,23,27,32,37,42,48,54,61,68,75,83])+      [wilcoxonMatchedPairCriticalValue x 0.005 | x <- [1..27]]+  ]+  where+    test n (a, b, c) = testEquality ("Wilcoxon Paired " ++ show n) c res+      where res = (wilcoxonMatchedPairSignedRank (U.fromList a) (U.fromList b))++    -- List of (Sample A, Sample B, (Positive Rank, Negative Rank))+    testData :: [([Double], [Double], (Double, Double))]+    testData = [ ([1..10], [1..10], (0, 0     ))+               , ([1..5],  [6..10], (0, 5*(-3)))+               -- Worked example from the Internet:+               , ( [125,115,130,140,140,115,140,125,140,135]+                 , [110,122,125,120,140,124,123,137,135,145]+                 , ( sum $ filter (> 0) [7,-3,1.5,9,0,-4,8,-6,1.5,-5]+                   , sum $ filter (< 0) [7,-3,1.5,9,0,-4,8,-6,1.5,-5]+                   )+                 )+               -- Worked examples from books/papers:+               , ( [2.4,1.9,2.3,1.9,2.4,2.5]+                 , [2.0,2.1,2.0,2.0,1.8,2.0]+                 , (18, -3)+                 )+               , ( [130,170,125,170,130,130,145,160]+                 , [120,163,120,135,143,136,144,120]+                 , (27, -9)+                 )+               , ( [540,580,600,680,430,740,600,690,605,520]+                 , [760,710,1105,880,500,990,1050,640,595,520]+                 , (3, -42)+                 )+               ]+    to4dp tgt x = x >= tgt - 0.00005 && x < tgt + 0.00005++++----------------------------------------------------------------+-- K-S test+----------------------------------------------------------------+++kolmogorovSmirnovDTest :: [Test]+kolmogorovSmirnovDTest =+  [ testAssertion "K-S D statistics" $+    and [ eq 1e-6 (kolmogorovSmirnovD standard (toU sample)) reference+        | (reference,sample) <- tableKSD+        ]+  , testAssertion "K-S 2-sample statistics" $+    and [ eq 1e-6 (kolmogorovSmirnov2D (toU xs) (toU ys)) reference+        | (reference,xs,ys) <- tableKS2D+        ]+  , testAssertion "K-S probability" $+    and [ eq 1e-14 (kolmogorovSmirnovProbability n d) p+        | (d,n,p) <- testData+        ]+  ]+  where+    toU = U.fromList+    -- Test data for the calculation of cumulative probability+    -- P(D[n] < d).+    --+    -- Test data is:+    --    (D[n], n, p)+    -- Table is generated using sample program from paper+    testData :: [(Double,Int,Double)]+    testData =+      [ (0.09           ,    3, 0                   )+      , (0.2            ,    3, 0.00177777777777778 )+      , (0.301          ,    3, 0.116357025777778   )+      , (0.392          ,    3, 0.383127210666667   )+      , (0.5003         ,    3, 0.667366306558667   )+      , (0.604          ,    3, 0.861569877333333   )+      , (0.699          ,    3, 0.945458198         )+      , (0.802          ,    3, 0.984475216         )+      , (0.9            ,    3, 0.998               )+      , (0.09           ,    5, 0                   )+      , (0.2            ,    5, 0.0384              )+      , (0.301          ,    5, 0.33993786080016    )+      , (0.392          ,    5, 0.66931908083712    )+      , (0.5003         ,    5, 0.888397260183794   )+      , (0.604          ,    5, 0.971609957879808   )+      , (0.699          ,    5, 0.994331075994008   )+      , (0.802          ,    5, 0.999391366368064   )+      , (0.9            ,    5, 0.99998             )+      , (0.09           ,    8, 3.37615237575e-06   )+      , (0.2            ,    8, 0.151622071801758   )+      , (0.301          ,    8, 0.613891042670582   )+      , (0.392          ,    8, 0.871491561427005   )+      , (0.5003         ,    8, 0.977534089199071   )+      , (0.604          ,    8, 0.997473116268255   )+      , (0.699          ,    8, 0.999806082005123   )+      , (0.802          ,    8, 0.999995133786947   )+      , (0.9            ,    8, 0.99999998          )+      , (0.09           ,   10, 3.89639433093119e-05)+      , (0.2            ,   10, 0.25128096          )+      , (0.301          ,   10, 0.732913126355935   )+      , (0.392          ,   10, 0.932185254518767   )+      , (0.5003         ,   10, 0.992276179340446   )+      , (0.604          ,   10, 0.999495533516769   )+      , (0.699          ,   10, 0.999979691783985   )+      , (0.802          ,   10, 0.999999801409237   )+      , (0.09           ,   20, 0.00794502217168886 )+      , (0.2            ,   20, 0.647279826376584   )+      , (0.301          ,   20, 0.958017466965765   )+      , (0.392          ,   20, 0.997206424843499   )+      , (0.5003         ,   20, 0.999962641414228   )+      , (0.09           ,   30, 0.0498147538075168  )+      , (0.2            ,   30, 0.842030838984526   )+      , (0.301          ,   30, 0.993403560017612   )+      , (0.392          ,   30, 0.99988478803318    )+      , (0.09           ,  100, 0.629367974413669   )+      ]
+ tests/Tests/NonParametric/Table.hs view
@@ -0,0 +1,39 @@+module Tests.NonParametric.Table (+      tableKSD+    , tableKS2D+    ) where++-- Table for Kolmogorov-Smirnov statistics for standard normal+-- distribution. Generated using R.+--+-- First element of tuple is D second is sample for which it was+-- calculated.+tableKSD :: [(Double,[Double])]+tableKSD =+  [ (0.2012078,[1.360645,-0.3151904,-1.245443,0.1741977,-0.1421206,-1.798246,1.171594,-1.335844,-5.050093e-2,1.030063,-1.849005,0.6491455,-0.7028004])+  , (0.2569956,[0.3884734,-1.227821,-0.4166262,0.429118,-0.9280124,0.8025867,-0.6703089,-0.2124872,0.1224496,0.1087734,-4.285284e-2,-1.039936,-0.7071956])+  , (0.1960356,[-1.814745,-0.6327167,0.7082493,0.6264716,1.02061,-0.4094635,0.821026,-0.4255047,-0.4820728,-0.2239833,0.648517,1.114283,0.3610216])+  , (0.2095746,[0.187011,0.1805498,0.4448389,0.6065506,0.2308673,0.5292549,-1.489902,-1.455191,0.5449396,-0.1436403,-0.7977073,-0.2693545,0.8260888,-1.474473,-2.158696e-2,-0.1455387])+  , (0.1922603,[0.5772317,-1.255561,1.605823,0.4923361,0.2470848,1.176101,-0.3767689,-0.6896885,0.4509345,-0.5048447,0.9436534,1.025599,0.2998393,-3.415219e-2,1.264315,-1.44433,-1.646449e-2])+  , (0.2173401,[1.812807,-0.8687497,-0.5710508,1.003647,1.142621,0.6546577,-6.083323e-3,1.628574e-2,1.067499,-1.953143,-0.6060077,1.90859,-0.7480553,0.6715162,-0.928759,1.862,1.604621,-0.2171044,-0.1835918])+  , (0.2510541,[-0.4769572,1.062319,0.9952284,1.198086,1.015589,-0.4154523,-0.6711762,1.202902,0.2217098,5.381759e-2,0.6679715,0.2551287,-0.1371492])+  , (0.1996022,[1.158607,-0.7354863,1.526559,-0.7855418,-2.82999,-0.6045106,-0.1830228,0.3306812,-0.819657,-1.223715,0.2536423,-0.4155781,1.447042])+  , (0.2284761,[1.239965,0.8187093,0.5199788,1.172072,0.748259,1.869376e-2,0.1625921,-1.712065,0.7043582,-1.702702,-0.4792806,-0.1023351,0.1187189])+  , (0.2337866,[0.9417261,-0.1024297,-0.7354359,1.099991,0.801984,-0.3745397,-1.749564,1.795771,1.099963,-0.605557,-2.035897,1.893603,-0.3468928,-0.2593938,2.100988,0.9665698,0.8757091,0.7696328,0.8730729,-0.3990352,2.04361,-0.4617864,-0.155021,2.15774,0.2687795,-0.9853512,-0.3264898,1.260026,4.267695,-0.5571145,0.6307067,-0.1691405,-1.730686])+  , (0.3389167,[2.025542,-1.542641,-1.090238,3.99027,9.949129e-2,-0.8974433,-2.508418,6.390346,-2.675515,1.154459,1.688072,2.220727,-0.4743102])+  , (0.4920231,[0.5192906,-3.260813,-1.245185,1.693084,3.561318,4.058924,2.27063,0.9446943,4.794159,-3.423733,0.8240817,0.644059,0.900175,1.932513,1.024586,2.82823,2.072192,-0.353231,-0.4319673,1.505952,1.0199,4.555054,2.364929,5.531467,3.279415,3.19821,2.726925,1.680027,-0.9041334,-0.8246765,-1.343979,8.454955,1.354581])+  , (0.6727408,[-6.705672,-3.193988,-4.612611,-3.207994,-5.070172,-6.141169,-0.397149,-4.093359,-1.204801,-3.986585,-2.724662,0.9868107,-6.295266,-5.95839,-6.35114,-1.679555,-2.635889,-4.050329,1.557428,-2.548465,-0.9073924,-1.502018,-4.535688,-4.158818,-8.833434,-5.944697,-1.569672,-4.70399,-7.832059,-4.093708,-8.393417,-2.085432,-7.06495,-0.4230419,-3.046822,-3.23895,-0.9265873,-9.227822,3.293713,-5.593577,-5.942398,-4.358421,2.660044,-4.301572,-1.258879,0.1499903,3.572833,-3.19844,0.8652432,-0.3025793,-1.576673,-7.666265,-6.751463,-1.398944,-2.690656,-1.429654,7.508364e-2,0.7998344,-3.562074,-1.021431,1.342968,2.110244,-7.561497,-2.372083,-3.649193,-5.7723,-1.068083,0.7537809,-4.569546,-1.198005,-5.638384,-1.227226,-1.195852,-1.118175,-9.130527,0.9675821,-2.497391,0.5988562,-1.965783,-4.25741,-6.547006,-1.459294,-2.380556,-3.977307,-7.809006,-4.276819,-4.028746,-9.055546,-3.599239,-1.470512,-8.253329,-1.351687,-4.269324,-6.140353,-6.30808,-1.834091,-3.135146,-9.391791,3.117815,-5.554733,-2.556769,-3.287376,-2.064013,-5.741995,-5.047918,-4.808841,-1.488526,-0.2351115,-5.760833,-2.722929,-7.012353,2.281171,-3.890514,-1.516824,-1.41011,-1.828457,-5.561244,-3.472142,-10.16919,-0.4369042,-5.698953,-4.587462,-4.897086])+  ]++-- Table for 2-sample Kolmogorov-Smirnov statistics. Generated using R+--+-- First element is D, second and third are samples+tableKS2D :: [(Double,[Double],[Double])]+tableKS2D =+  [ (0.2820513,[-0.4212928,2.146532,0.7585263,-0.5086105,-0.7725486,6.235548e-2,-0.1849861,0.861972,-0.1958534,-3.379697e-2,-1.316854,0.6701269],[0.4957582,0.4241167,0.9822869,0.4504248,-0.1749617,1.178098,-1.117222,-0.859273,0.3073736,0.4344583,-0.4761338,-1.332374,1.487291])+  , (0.2820513,[-0.712252,0.7990333,-0.7968473,1.443609,1.163096,-1.349071,-0.1553941,-2.003104,-0.3400618,-0.7019282,0.183293,-0.2352167],[-0.4622455,-0.8132221,0.1161614,-1.472115e-2,1.001454,-6.557789e-2,-0.2531216,-1.032432,0.4105478,1.749614,0.9722899,5.850942e-2,-0.3352746])+  , (0.2564103,[0.3509882,-0.2982833,1.314731,1.264223,-0.8156374,0.3734029,-3.288915e-2,0.6766016,0.9786335,0.1079949,-0.4211722,1.58656],[0.8024675,7.464538e-2,0.2739861,-2.334255e-2,0.5611802,0.6683374,0.4358206,0.349843,1.207834,1.402578,-0.4049183,0.4286042,1.665129])+  , (0.1833333,[1.376196,9.926384e-2,2.199292,-2.04993,0.5585353,-0.4812132,0.1041527,2.084774,0.71194,-1.398245,-4.458574e-2,1.484945,-1.473182,1.020076,-0.7019646,0.2182066,-1.702963,-0.3522622,-0.8129267,-0.6338972],[-1.020371,0.3323861,1.513288,0.1958708,-1.0723,5.323446e-2,-0.9993713,-0.7046356,-0.6781067,-0.4471603,1.512042,-0.2650665,-4.765228e-2,-1.501205,1.228664,0.5332935,-0.2960315,-0.1509683])+  , (0.5666667,[0.7145305,0.1255674,2.001531,0.1419216],[2.113474,-0.3352839,-0.4962429,-1.386079,0.6404667,-0.7145304,0.1084008,-0.9821421,-2.270472,-1.003846,-0.5644588,2.699695,-1.296494,-0.1538839,1.319094,-1.127544,0.3568889,0.2004726,-1.313291,0.3581084,0.3313498,0.9336278,0.9850203,-1.309506,1.170459,-0.7517466,-1.771269,0.7156381,-1.129691,0.877729])+  , (0.5,[0.6950626,0.1643805,-0.3102472,0.4810762,0.1844602,1.338836,-0.8083386,-0.5482141,0.9532421,-0.2644837],[7.527945,-1.95654,1.513725,-1.318431,2.453895,0.2078194,0.7371092,2.834245,-2.134794,3.938259])+  ]
− tests/Tests/NonparametricTest.hs 
@@ -1,233 +0,0 @@--- Tests for Statistics.Test.NonParametric-module Tests.NonparametricTest (-  nonparametricTests-  ) where---import qualified Data.Vector.Unboxed as U-import Test.HUnit                     (assertEqual)-import Test.Framework-import Test.Framework.Providers.HUnit--import Statistics.Test.MannWhitneyU-import Statistics.Test.WilcoxonT--import Tests.Helpers-import Tests.NonparametricTest.Table--import Statistics.Test.KolmogorovSmirnov-import Statistics.Distribution.Normal    (standard)----nonparametricTests :: Test-nonparametricTests = testGroup "Nonparametric tests"-                   $ concat [ mannWhitneyTests-                            , wilcoxonSumTests-                            , wilcoxonPairTests-                            , kolmogorovSmirnovDTest-                            ]--------------------------------------------------------------------mannWhitneyTests :: [Test]-mannWhitneyTests = zipWith test [(0::Int)..] testData ++-  [ testEquality "Mann-Whitney U Critical Values, m=1"-      (replicate (20*3) Nothing)-      [mannWhitneyUCriticalValue (1,x) p | x <- [1..20], p <- [0.005,0.01,0.025]]-  , testEquality "Mann-Whitney U Critical Values, m=2, p=0.025"-      (replicate 7 Nothing ++ map Just [0,0,0,0,1,1,1,1,1,2,2,2,2])-      [mannWhitneyUCriticalValue (2,x) 0.025 | x <- [1..20]]-  , testEquality "Mann-Whitney U Critical Values, m=6, p=0.05"-      (replicate 1 Nothing ++ map Just [0, 2,3,5,7,8,10,12,14,16,17,19,21,23,25,26,28,30,32])-      [mannWhitneyUCriticalValue (6,x) 0.05 | x <- [1..20]]-  , testEquality "Mann-Whitney U Critical Values, m=20, p=0.025"-      (replicate 1 Nothing ++ map Just [2,8,14,20,27,34,41,48,55,62,69,76,83,90,98,105,112,119,127])-      [mannWhitneyUCriticalValue (20,x) 0.025 | x <- [1..20]]-  ]-  where-    test n (a, b, c, d)-      = testCase "Mann-Whitney" $ do-          assertEqual ("Mann-Whitney U "     ++ show n) c us-          assertEqual ("Mann-Whitney U Sig " ++ show n) d ss-      where-        us = mannWhitneyU (U.fromList a) (U.fromList b)-        ss = mannWhitneyUSignificant TwoTailed (length a, length b) 0.05 us-    -- List of (Sample A, Sample B, (Positive Rank, Negative Rank))-    testData :: [([Double], [Double], (Double, Double), Maybe TestResult)]-    testData = [ ( [3,4,2,6,2,5]-                 , [9,7,5,10,6,8]-                 , (2, 34)-                 , Just Significant-                 )-               , ( [540,480,600,590,605]-                 , [760,890,1105,595,940]-                 , (2, 23)-                 , Just Significant-                 )-               , ( [19,22,16,29,24]-                 , [20,11,17,12]-                 , (17, 3)-                 , Just NotSignificant-                 )-               , ( [126,148,85,61, 179,93, 45,189,85,93]-                 , [194,128,69,135,171,149,89,248,79,137]-                 , (35,65)-                 , Just NotSignificant-                 )-               , ( [1..30]-                 , [1..30]-                 , (450,450)-                 , Just NotSignificant-                 )-               , ( [1 .. 30]-                 , [11.5 .. 40 ]-                 , (190.0,710.0)-                 , Just Significant-                 )-               ]--wilcoxonSumTests :: [Test]-wilcoxonSumTests = zipWith test [(0::Int)..] testData-  where-    test n (a, b, c) = testCase "Wilcoxon Sum"-                     $ assertEqual ("Wilcoxon Sum " ++ show n) c (wilcoxonRankSums (U.fromList a) (U.fromList b))-    -- List of (Sample A, Sample B, (Positive Rank, Negative Rank))-    testData :: [([Double], [Double], (Double, Double))]-    testData = [ ( [8.50,9.48,8.65,8.16,8.83,7.76,8.63]-                 , [8.27,8.20,8.25,8.14,9.00,8.10,7.20,8.32,7.70]-                 , (75, 61)-                 )-               , ( [0.45,0.50,0.61,0.63,0.75,0.85,0.93]-                 , [0.44,0.45,0.52,0.53,0.56,0.58,0.58,0.65,0.79]-                 , (71.5, 64.5)-                 )-               ]--wilcoxonPairTests :: [Test]-wilcoxonPairTests = zipWith test [(0::Int)..] testData ++-  -- Taken from the Mitic paper:-  [ testAssertion "Sig 16, 35" (to4dp 0.0467 $ wilcoxonMatchedPairSignificance 16 35)-  , testAssertion "Sig 16, 36" (to4dp 0.0523 $ wilcoxonMatchedPairSignificance 16 36)-  , testEquality   "Wilcoxon critical values, p=0.05"-      (replicate 4 Nothing ++ map Just [0,2,3,5,8,10,13,17,21,25,30,35,41,47,53,60,67,75,83,91,100,110,119])-      [wilcoxonMatchedPairCriticalValue x 0.05 | x <- [1..27]]-  , testEquality "Wilcoxon critical values, p=0.025"-      (replicate 5 Nothing ++ map Just [0,2,3,5,8,10,13,17,21,25,29,34,40,46,52,58,65,73,81,89,98,107])-      [wilcoxonMatchedPairCriticalValue x 0.025 | x <- [1..27]]-  , testEquality "Wilcoxon critical values, p=0.01"-      (replicate 6 Nothing ++ map Just [0,1,3,5,7,9,12,15,19,23,27,32,37,43,49,55,62,69,76,84,92])-      [wilcoxonMatchedPairCriticalValue x 0.01 | x <- [1..27]]-  , testEquality "Wilcoxon critical values, p=0.005"-      (replicate 7 Nothing ++ map Just [0,1,3,5,7,9,12,15,19,23,27,32,37,42,48,54,61,68,75,83])-      [wilcoxonMatchedPairCriticalValue x 0.005 | x <- [1..27]]-  ]-  where-    test n (a, b, c) = testEquality ("Wilcoxon Paired " ++ show n) c res-      where res = (wilcoxonMatchedPairSignedRank (U.fromList a) (U.fromList b))--    -- List of (Sample A, Sample B, (Positive Rank, Negative Rank))-    testData :: [([Double], [Double], (Double, Double))]-    testData = [ ([1..10], [1..10], (0, 0     ))-               , ([1..5],  [6..10], (0, 5*(-3)))-               -- Worked example from the Internet:-               , ( [125,115,130,140,140,115,140,125,140,135]-                 , [110,122,125,120,140,124,123,137,135,145]-                 , ( sum $ filter (> 0) [7,-3,1.5,9,0,-4,8,-6,1.5,-5]-                   , sum $ filter (< 0) [7,-3,1.5,9,0,-4,8,-6,1.5,-5]-                   )-                 )-               -- Worked examples from books/papers:-               , ( [2.4,1.9,2.3,1.9,2.4,2.5]-                 , [2.0,2.1,2.0,2.0,1.8,2.0]-                 , (18, -3)-                 )-               , ( [130,170,125,170,130,130,145,160]-                 , [120,163,120,135,143,136,144,120]-                 , (27, -9)-                 )-               , ( [540,580,600,680,430,740,600,690,605,520]-                 , [760,710,1105,880,500,990,1050,640,595,520]-                 , (3, -42)-                 )-               ]-    to4dp tgt x = x >= tgt - 0.00005 && x < tgt + 0.00005----------------------------------------------------------------------- K-S test--------------------------------------------------------------------kolmogorovSmirnovDTest :: [Test]-kolmogorovSmirnovDTest =-  [ testAssertion "K-S D statistics" $-    and [ eq 1e-6 (kolmogorovSmirnovD standard (toU sample)) reference-        | (reference,sample) <- tableKSD-        ]-  , testAssertion "K-S 2-sample statistics" $-    and [ eq 1e-6 (kolmogorovSmirnov2D (toU xs) (toU ys)) reference-        | (reference,xs,ys) <- tableKS2D-        ]-  , testAssertion "K-S probability" $-    and [ eq 1e-14 (kolmogorovSmirnovProbability n d) p-        | (d,n,p) <- testData-        ]-  ]-  where-    toU = U.fromList-    -- Test data for the calculation of cumulative probability -    -- P(D[n] < d).-    -- -    -- Test data is:-    --    (D[n], n, p)-    -- Table is generated using sample program from paper-    testData :: [(Double,Int,Double)]-    testData = -      [ (0.09           ,    3, 0                   )-      , (0.2            ,    3, 0.00177777777777778 )-      , (0.301          ,    3, 0.116357025777778   )-      , (0.392          ,    3, 0.383127210666667   )-      , (0.5003         ,    3, 0.667366306558667   )-      , (0.604          ,    3, 0.861569877333333   )-      , (0.699          ,    3, 0.945458198         )-      , (0.802          ,    3, 0.984475216         )-      , (0.9            ,    3, 0.998               )-      , (0.09           ,    5, 0                   )-      , (0.2            ,    5, 0.0384              )-      , (0.301          ,    5, 0.33993786080016    )-      , (0.392          ,    5, 0.66931908083712    )-      , (0.5003         ,    5, 0.888397260183794   )-      , (0.604          ,    5, 0.971609957879808   )-      , (0.699          ,    5, 0.994331075994008   )-      , (0.802          ,    5, 0.999391366368064   )-      , (0.9            ,    5, 0.99998             )-      , (0.09           ,    8, 3.37615237575e-06   )-      , (0.2            ,    8, 0.151622071801758   )-      , (0.301          ,    8, 0.613891042670582   )-      , (0.392          ,    8, 0.871491561427005   )-      , (0.5003         ,    8, 0.977534089199071   )-      , (0.604          ,    8, 0.997473116268255   )-      , (0.699          ,    8, 0.999806082005123   )-      , (0.802          ,    8, 0.999995133786947   )-      , (0.9            ,    8, 0.99999998          )-      , (0.09           ,   10, 3.89639433093119e-05)-      , (0.2            ,   10, 0.25128096          )-      , (0.301          ,   10, 0.732913126355935   )-      , (0.392          ,   10, 0.932185254518767   )-      , (0.5003         ,   10, 0.992276179340446   )-      , (0.604          ,   10, 0.999495533516769   )-      , (0.699          ,   10, 0.999979691783985   )-      , (0.802          ,   10, 0.999999801409237   )-      , (0.09           ,   20, 0.00794502217168886 )-      , (0.2            ,   20, 0.647279826376584   )-      , (0.301          ,   20, 0.958017466965765   )-      , (0.392          ,   20, 0.997206424843499   )-      , (0.5003         ,   20, 0.999962641414228   )-      , (0.09           ,   30, 0.0498147538075168  )-      , (0.2            ,   30, 0.842030838984526   )-      , (0.301          ,   30, 0.993403560017612   )-      , (0.392          ,   30, 0.99988478803318    )-      , (0.09           ,  100, 0.629367974413669   )-      ]
− tests/Tests/NonparametricTest/Table.hs 
@@ -1,36 +0,0 @@-module Tests.NonparametricTest.Table where---- Table for Kolmogorov-Smirnov statistics for standard normal--- distribution. Generated using R.------ First element of tuple is D second is sample for which it was--- calculated. -tableKSD :: [(Double,[Double])]-tableKSD = -  [ (0.2012078,[1.360645,-0.3151904,-1.245443,0.1741977,-0.1421206,-1.798246,1.171594,-1.335844,-5.050093e-2,1.030063,-1.849005,0.6491455,-0.7028004])-  , (0.2569956,[0.3884734,-1.227821,-0.4166262,0.429118,-0.9280124,0.8025867,-0.6703089,-0.2124872,0.1224496,0.1087734,-4.285284e-2,-1.039936,-0.7071956])-  , (0.1960356,[-1.814745,-0.6327167,0.7082493,0.6264716,1.02061,-0.4094635,0.821026,-0.4255047,-0.4820728,-0.2239833,0.648517,1.114283,0.3610216])-  , (0.2095746,[0.187011,0.1805498,0.4448389,0.6065506,0.2308673,0.5292549,-1.489902,-1.455191,0.5449396,-0.1436403,-0.7977073,-0.2693545,0.8260888,-1.474473,-2.158696e-2,-0.1455387])-  , (0.1922603,[0.5772317,-1.255561,1.605823,0.4923361,0.2470848,1.176101,-0.3767689,-0.6896885,0.4509345,-0.5048447,0.9436534,1.025599,0.2998393,-3.415219e-2,1.264315,-1.44433,-1.646449e-2])-  , (0.2173401,[1.812807,-0.8687497,-0.5710508,1.003647,1.142621,0.6546577,-6.083323e-3,1.628574e-2,1.067499,-1.953143,-0.6060077,1.90859,-0.7480553,0.6715162,-0.928759,1.862,1.604621,-0.2171044,-0.1835918])-  , (0.2510541,[-0.4769572,1.062319,0.9952284,1.198086,1.015589,-0.4154523,-0.6711762,1.202902,0.2217098,5.381759e-2,0.6679715,0.2551287,-0.1371492])-  , (0.1996022,[1.158607,-0.7354863,1.526559,-0.7855418,-2.82999,-0.6045106,-0.1830228,0.3306812,-0.819657,-1.223715,0.2536423,-0.4155781,1.447042])-  , (0.2284761,[1.239965,0.8187093,0.5199788,1.172072,0.748259,1.869376e-2,0.1625921,-1.712065,0.7043582,-1.702702,-0.4792806,-0.1023351,0.1187189])-  , (0.2337866,[0.9417261,-0.1024297,-0.7354359,1.099991,0.801984,-0.3745397,-1.749564,1.795771,1.099963,-0.605557,-2.035897,1.893603,-0.3468928,-0.2593938,2.100988,0.9665698,0.8757091,0.7696328,0.8730729,-0.3990352,2.04361,-0.4617864,-0.155021,2.15774,0.2687795,-0.9853512,-0.3264898,1.260026,4.267695,-0.5571145,0.6307067,-0.1691405,-1.730686])-  , (0.3389167,[2.025542,-1.542641,-1.090238,3.99027,9.949129e-2,-0.8974433,-2.508418,6.390346,-2.675515,1.154459,1.688072,2.220727,-0.4743102])-  , (0.4920231,[0.5192906,-3.260813,-1.245185,1.693084,3.561318,4.058924,2.27063,0.9446943,4.794159,-3.423733,0.8240817,0.644059,0.900175,1.932513,1.024586,2.82823,2.072192,-0.353231,-0.4319673,1.505952,1.0199,4.555054,2.364929,5.531467,3.279415,3.19821,2.726925,1.680027,-0.9041334,-0.8246765,-1.343979,8.454955,1.354581])-  , (0.6727408,[-6.705672,-3.193988,-4.612611,-3.207994,-5.070172,-6.141169,-0.397149,-4.093359,-1.204801,-3.986585,-2.724662,0.9868107,-6.295266,-5.95839,-6.35114,-1.679555,-2.635889,-4.050329,1.557428,-2.548465,-0.9073924,-1.502018,-4.535688,-4.158818,-8.833434,-5.944697,-1.569672,-4.70399,-7.832059,-4.093708,-8.393417,-2.085432,-7.06495,-0.4230419,-3.046822,-3.23895,-0.9265873,-9.227822,3.293713,-5.593577,-5.942398,-4.358421,2.660044,-4.301572,-1.258879,0.1499903,3.572833,-3.19844,0.8652432,-0.3025793,-1.576673,-7.666265,-6.751463,-1.398944,-2.690656,-1.429654,7.508364e-2,0.7998344,-3.562074,-1.021431,1.342968,2.110244,-7.561497,-2.372083,-3.649193,-5.7723,-1.068083,0.7537809,-4.569546,-1.198005,-5.638384,-1.227226,-1.195852,-1.118175,-9.130527,0.9675821,-2.497391,0.5988562,-1.965783,-4.25741,-6.547006,-1.459294,-2.380556,-3.977307,-7.809006,-4.276819,-4.028746,-9.055546,-3.599239,-1.470512,-8.253329,-1.351687,-4.269324,-6.140353,-6.30808,-1.834091,-3.135146,-9.391791,3.117815,-5.554733,-2.556769,-3.287376,-2.064013,-5.741995,-5.047918,-4.808841,-1.488526,-0.2351115,-5.760833,-2.722929,-7.012353,2.281171,-3.890514,-1.516824,-1.41011,-1.828457,-5.561244,-3.472142,-10.16919,-0.4369042,-5.698953,-4.587462,-4.897086])-  ]---- Table for 2-sample Kolmogorov-Smirnov statistics. Generated using R------ First element is D, second and third are samples-tableKS2D :: [(Double,[Double],[Double])]-tableKS2D =-  [ (0.2820513,[-0.4212928,2.146532,0.7585263,-0.5086105,-0.7725486,6.235548e-2,-0.1849861,0.861972,-0.1958534,-3.379697e-2,-1.316854,0.6701269],[0.4957582,0.4241167,0.9822869,0.4504248,-0.1749617,1.178098,-1.117222,-0.859273,0.3073736,0.4344583,-0.4761338,-1.332374,1.487291])-  , (0.2820513,[-0.712252,0.7990333,-0.7968473,1.443609,1.163096,-1.349071,-0.1553941,-2.003104,-0.3400618,-0.7019282,0.183293,-0.2352167],[-0.4622455,-0.8132221,0.1161614,-1.472115e-2,1.001454,-6.557789e-2,-0.2531216,-1.032432,0.4105478,1.749614,0.9722899,5.850942e-2,-0.3352746])-  , (0.2564103,[0.3509882,-0.2982833,1.314731,1.264223,-0.8156374,0.3734029,-3.288915e-2,0.6766016,0.9786335,0.1079949,-0.4211722,1.58656],[0.8024675,7.464538e-2,0.2739861,-2.334255e-2,0.5611802,0.6683374,0.4358206,0.349843,1.207834,1.402578,-0.4049183,0.4286042,1.665129])-  , (0.1833333,[1.376196,9.926384e-2,2.199292,-2.04993,0.5585353,-0.4812132,0.1041527,2.084774,0.71194,-1.398245,-4.458574e-2,1.484945,-1.473182,1.020076,-0.7019646,0.2182066,-1.702963,-0.3522622,-0.8129267,-0.6338972],[-1.020371,0.3323861,1.513288,0.1958708,-1.0723,5.323446e-2,-0.9993713,-0.7046356,-0.6781067,-0.4471603,1.512042,-0.2650665,-4.765228e-2,-1.501205,1.228664,0.5332935,-0.2960315,-0.1509683])-  , (0.5666667,[0.7145305,0.1255674,2.001531,0.1419216],[2.113474,-0.3352839,-0.4962429,-1.386079,0.6404667,-0.7145304,0.1084008,-0.9821421,-2.270472,-1.003846,-0.5644588,2.699695,-1.296494,-0.1538839,1.319094,-1.127544,0.3568889,0.2004726,-1.313291,0.3581084,0.3313498,0.9336278,0.9850203,-1.309506,1.170459,-0.7517466,-1.771269,0.7156381,-1.129691,0.877729])-  , (0.5,[0.6950626,0.1643805,-0.3102472,0.4810762,0.1844602,1.338836,-0.8083386,-0.5482141,0.9532421,-0.2644837],[7.527945,-1.95654,1.513725,-1.318431,2.453895,0.2078194,0.7371092,2.834245,-2.134794,3.938259])-  ]
tests/Tests/Transform.hs view
@@ -6,26 +6,21 @@       tests     ) where -import Data.Bits             ((.&.), shiftL)-import Data.Complex          (Complex((:+)))-import Data.Functor          ((<$>))-import Statistics.Function   (within)-import Statistics.Transform--import Test.Framework                       (Test, testGroup)+import Data.Bits ((.&.), shiftL)+import Data.Complex (Complex((:+)))+import Data.Functor ((<$>))+import Numeric.Sum (kbn, sumVector)+import Statistics.Function (within)+import Statistics.Transform (CD, dct, fft, idct, ifft)+import Test.Framework (Test, testGroup) import Test.Framework.Providers.QuickCheck2 (testProperty)-import Test.QuickCheck                      (Positive(..),Property,Arbitrary(..),Gen,choose,vectorOf,-                                             printTestCase, quickCheck)--import Text.Printf-+import Test.QuickCheck (Positive(..), Property, Arbitrary(..), Gen, choose, vectorOf, printTestCase)+import Tests.Helpers (testAssertion)+import Text.Printf (printf) import qualified Data.Vector.Generic as G import qualified Data.Vector.Unboxed as U -import Tests.Helpers -- tests :: Test tests = testGroup "fft" [           testProperty "t_impulse"        t_impulse@@ -138,10 +133,10 @@   vectorNorm :: a -> Double  instance HasNorm (U.Vector Double) where-  vectorNorm = sqrt . U.sum . U.map (\x -> x*x)+  vectorNorm = sqrt . sumVector kbn . U.map (\x -> x*x)  instance HasNorm (U.Vector CD) where-  vectorNorm = sqrt . U.sum . U.map (\(x :+ y) -> x*x + y*y)+  vectorNorm = sqrt . sumVector kbn . U.map (\(x :+ y) -> x*x + y*y)  -- Approximate equality for vectors vecEqual :: Double -> U.Vector Double -> U.Vector Double -> Bool
tests/tests.hs view
@@ -1,15 +1,14 @@-import Test.Framework       (defaultMain)--import Tests.Distribution-import Tests.NonparametricTest-import qualified Tests.Transform-import qualified Tests.Function-import qualified Tests.KDE+import Test.Framework (defaultMain)+import qualified Tests.Distribution as Distribution+import qualified Tests.Function as Function+import qualified Tests.KDE as KDE+import qualified Tests.NonParametric as NonParametric+import qualified Tests.Transform as Transform  main :: IO ()-main = defaultMain [ distributionTests -                   , nonparametricTests-                   , Tests.Transform.tests-                   , Tests.Function.tests-                   , Tests.KDE.tests+main = defaultMain [ Distribution.tests+                   , Function.tests+                   , KDE.tests+                   , NonParametric.tests+                   , Transform.tests                    ]