| Copyright | (c) 2011 Aleksey Khudyakov |
|---|---|
| License | BSD3 |
| Maintainer | bos@serpentine.com |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | None |
| Language | Haskell98 |
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.
- kolmogorovSmirnovTest :: Distribution d => d -> Double -> Sample -> TestResult
- kolmogorovSmirnovTestCdf :: (Double -> Double) -> Double -> Sample -> TestResult
- kolmogorovSmirnovTest2 :: Double -> Sample -> Sample -> TestResult
- kolmogorovSmirnovCdfD :: (Double -> Double) -> Sample -> Double
- kolmogorovSmirnovD :: Distribution d => d -> Sample -> Double
- kolmogorovSmirnov2D :: Sample -> Sample -> Double
- kolmogorovSmirnovProbability :: Int -> Double -> Double
- data TestType
- data TestResult
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
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.
Calculate Kolmogorov's statistic D for two data samples. If either of samples is empty returns 0.
Probablities
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
data TestResult
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).