statistics-0.13.2.0: A library of statistical types, data, and functions

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Statistics.Test.KolmogorovSmirnov

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

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.

Arguments

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

Variant of `kolmogorovSmirnovTest` which uses CFD in form of function.

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

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.

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.

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

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 Source

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

data TestResult Source

Result of hypothesis testing

Constructors

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

# References

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