Statistics.Test.KolmogorovSmirnov

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.

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

FromJSON TestType

Methods

parseJSON :: Value -> Parser TestType

type Rep TestType

type Rep TestType = D1 (MetaData "TestType" "Statistics.Test.Types" "statistics-0.13.3.0-4cjYwUsSjEQGDMfnb5oeqe" 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

FromJSON TestResult

Methods

parseJSON :: Value -> Parser TestResult

type Rep TestResult

type Rep TestResult = D1 (MetaData "TestResult" "Statistics.Test.Types" "statistics-0.13.3.0-4cjYwUsSjEQGDMfnb5oeqe" 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).