statistics-0.10.1.0: 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.

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

Instances

 Eq TestType Ord TestType Show TestType Typeable TestType

data TestResult Source

Result of hypothesis testing

Constructors

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

Instances

 Eq TestResult Ord TestResult Show TestResult Typeable TestResult

References

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