Copyright	(c) 2011 Aleksey Khudyakov
License	BSD3
Maintainer	bos@serpentine.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Statistics.Test.KolmogorovSmirnov

Contents

Kolmogorov-Smirnov test
Evaluate statistics
Probabilities
References

Description

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

Synopsis

kolmogorovSmirnovTest :: (Distribution d, Vector v Double) => d -> v Double -> Maybe (Test ())
kolmogorovSmirnovTestCdf :: Vector v Double => (Double -> Double) -> v Double -> Maybe (Test ())
kolmogorovSmirnovTest2 :: Vector v Double => v Double -> v Double -> Maybe (Test ())
kolmogorovSmirnovCdfD :: Vector v Double => (Double -> Double) -> v Double -> Double
kolmogorovSmirnovD :: (Distribution d, Vector v Double) => d -> v Double -> Double
kolmogorovSmirnov2D :: Vector v Double => v Double -> v Double -> Double
kolmogorovSmirnovProbability :: Int -> Double -> Double
module Statistics.Test.Types

Kolmogorov-Smirnov test

kolmogorovSmirnovTest Source #

Arguments

:: (Distribution d, Vector v Double)
=> d	Distribution
-> v Double	Data sample
-> Maybe (Test ())

Check that sample could be described by distribution. Returns Nothing is sample is empty

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

kolmogorovSmirnovTestCdf Source #

Arguments

:: Vector v Double
=> (Double -> Double)	CDF of distribution
-> v Double	Data sample
-> Maybe (Test ())

Variant of kolmogorovSmirnovTest which uses CDF in form of function.

kolmogorovSmirnovTest2 Source #

Arguments

:: Vector v Double
=> v Double	Sample 1
-> v Double	Sample 2
-> Maybe (Test ())

Two sample Kolmogorov-Smirnov test. It tests whether two data samples could be described by the same distribution without making any assumptions about it. If either of samples is empty returns Nothing.

This test uses approximate formula for computing p-value.

Evaluate statistics

kolmogorovSmirnovCdfD Source #

Arguments

:: Vector v Double
=> (Double -> Double)	CDF function
-> v Double	Sample
-> Double

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

kolmogorovSmirnovD Source #

Arguments

:: (Distribution d, Vector v Double)
=> d	Distribution
-> v Double	Sample
-> Double

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

kolmogorovSmirnov2D Source #

Arguments

:: Vector v Double
=> v Double	First sample
-> v Double	Second sample
-> Double

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

Probabilities

kolmogorovSmirnovProbability Source #

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.

References

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

module Statistics.Test.Types