statistics-0.15.2.0: A library of statistical types, data, and functions

Statistics.Test.KolmogorovSmirnov

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

# Kolmogorov-Smirnov test

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.

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.

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

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.

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.

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.

# Probablities

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).