Copyright	(c) 2011 Aleksey Khudyakov
License	BSD3
Maintainer	bos@serpentine.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

Statistics.Test.KolmogorovSmirnov

Contents

Kolmogorov-Smirnov test
Evaluate statistics
Probablities
Data types
References

Description

Kolmogov-Smirnov tests are non-parametric tests for assesing whether given sample could be described by distribution or whether two samples have the same distribution. It's only applicable to continous distributions.

Synopsis

Kolmogorov-Smirnov test

kolmogorovSmirnovTest #

Arguments

:: Distribution d
=> d	Distribution
-> Double	p-value
-> Sample	Data sample
-> TestResult

Check that sample could be described by distribution. Significant means distribution is not compatible with data for given p-value.

This test uses Marsaglia-Tsang-Wang exact alogorithm for calculation of p-value.

kolmogorovSmirnovTestCdf #

Arguments

:: (Double -> Double)	CDF of distribution
-> Double	p-value
-> Sample	Data sample
-> TestResult

Variant of kolmogorovSmirnovTest which uses CFD in form of function.

kolmogorovSmirnovTest2 #

Arguments

:: Double	p-value
-> Sample	Sample 1
-> Sample	Sample 2
-> TestResult

Two sample Kolmogorov-Smirnov test. It tests whether two data samples could be described by the same distribution without making any assumptions about it.

This test uses approxmate formula for computing p-value.

Evaluate statistics

kolmogorovSmirnovCdfD #

Arguments

:: (Double -> Double)	CDF function
-> Sample	Sample
-> Double

Calculate Kolmogorov's statistic D for given cumulative distribution function (CDF) and data sample. If sample is empty returns 0.

kolmogorovSmirnovD #

Arguments

:: Distribution d
=> d	Distribution
-> Sample	Sample
-> Double

Calculate Kolmogorov's statistic D for given cumulative distribution function (CDF) and data sample. If sample is empty returns 0.

kolmogorovSmirnov2D #

Arguments

:: Sample	First sample
-> Sample	Second sample
-> Double

Calculate Kolmogorov's statistic D for two data samples. If either of samples is empty returns 0.

Probablities

kolmogorovSmirnovProbability #

Arguments

:: Int	Size of the sample
-> Double	D value
-> Double

Calculate cumulative probability function for Kolmogorov's distribution with n parameters or probability of getting value smaller than d with n-elements sample.

It uses algorithm by Marsgalia et. al. and provide at least 7-digit accuracy.

Data types

data TestType #

Test type. Exact meaning depends on a specific test. But generally it's tested whether some statistics is too big (small) for OneTailed or whether it too big or too small for TwoTailed

Constructors

OneTailed
TwoTailed

Instances

Eq TestType #
Methods (==) :: TestType -> TestType -> Bool # (/=) :: TestType -> TestType -> Bool #
Data TestType #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TestType -> c TestType # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TestType # toConstr :: TestType -> Constr # dataTypeOf :: TestType -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c TestType) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TestType) # gmapT :: (forall b. Data b => b -> b) -> TestType -> TestType # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TestType -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TestType -> r # gmapQ :: (forall d. Data d => d -> u) -> TestType -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> TestType -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> TestType -> m TestType # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> TestType -> m TestType # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> TestType -> m TestType #
Ord TestType #
Methods compare :: TestType -> TestType -> Ordering # (<) :: TestType -> TestType -> Bool # (<=) :: TestType -> TestType -> Bool # (>) :: TestType -> TestType -> Bool # (>=) :: TestType -> TestType -> Bool # max :: TestType -> TestType -> TestType # min :: TestType -> TestType -> TestType #
Show TestType #
Methods showsPrec :: Int -> TestType -> ShowS # show :: TestType -> String # showList :: [TestType] -> ShowS #
Generic TestType #
Associated Types type Rep TestType :: * -> * # Methods from :: TestType -> Rep TestType x # to :: Rep TestType x -> TestType #
ToJSON TestType #
Methods toJSON :: TestType -> Value # toEncoding :: TestType -> Encoding # toJSONList :: [TestType] -> Value # toEncodingList :: [TestType] -> Encoding #
FromJSON TestType #
Methods parseJSON :: Value -> Parser TestType # parseJSONList :: Value -> Parser [TestType] #
type Rep TestType #
type Rep TestType = D1 (MetaData "TestType" "Statistics.Test.Types" "statistics-0.13.3.0-BiEAUT1kslI4cQhfIgfmy" False) ((:+:) (C1 (MetaCons "OneTailed" PrefixI False) U1) (C1 (MetaCons "TwoTailed" PrefixI False) U1))

data TestResult #

Result of hypothesis testing

Constructors

Significant	Null hypothesis should be rejected
NotSignificant	Data is compatible with hypothesis

Instances

Eq TestResult #
Methods (==) :: TestResult -> TestResult -> Bool # (/=) :: TestResult -> TestResult -> Bool #
Data TestResult #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TestResult -> c TestResult # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TestResult # toConstr :: TestResult -> Constr # dataTypeOf :: TestResult -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c TestResult) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TestResult) # gmapT :: (forall b. Data b => b -> b) -> TestResult -> TestResult # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TestResult -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TestResult -> r # gmapQ :: (forall d. Data d => d -> u) -> TestResult -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> TestResult -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> TestResult -> m TestResult # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> TestResult -> m TestResult # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> TestResult -> m TestResult #
Ord TestResult #
Methods compare :: TestResult -> TestResult -> Ordering # (<) :: TestResult -> TestResult -> Bool # (<=) :: TestResult -> TestResult -> Bool # (>) :: TestResult -> TestResult -> Bool # (>=) :: TestResult -> TestResult -> Bool # max :: TestResult -> TestResult -> TestResult # min :: TestResult -> TestResult -> TestResult #
Show TestResult #
Methods showsPrec :: Int -> TestResult -> ShowS # show :: TestResult -> String # showList :: [TestResult] -> ShowS #
Generic TestResult #
Associated Types type Rep TestResult :: * -> * # Methods from :: TestResult -> Rep TestResult x # to :: Rep TestResult x -> TestResult #
ToJSON TestResult #
Methods toJSON :: TestResult -> Value # toEncoding :: TestResult -> Encoding # toJSONList :: [TestResult] -> Value # toEncodingList :: [TestResult] -> Encoding #
FromJSON TestResult #
Methods parseJSON :: Value -> Parser TestResult # parseJSONList :: Value -> Parser [TestResult] #
type Rep TestResult #
type Rep TestResult = D1 (MetaData "TestResult" "Statistics.Test.Types" "statistics-0.13.3.0-BiEAUT1kslI4cQhfIgfmy" False) ((:+:) (C1 (MetaCons "Significant" PrefixI False) U1) (C1 (MetaCons "NotSignificant" PrefixI False) U1))

References

G. Marsaglia, W. W. Tsang, J. Wang (2003) Evaluating Kolmogorov's distribution, Journal of Statistical Software, American Statistical Association, vol. 8(i18).