KolmogorovSmirnovTest

KolmogorovSmirnovTest[data]
tests whether data is normally distributed using the KolmogorovSmirnov test.

KolmogorovSmirnovTest[data,dist]
tests whether data is distributed according to dist using the KolmogorovSmirnov test.

KolmogorovSmirnovTest[data,dist,"property"]
returns the value of .

Details and OptionsDetails and Options

  • KolmogorovSmirnovTest performs the KolmogorovSmirnov goodness-of-fit test with null hypothesis that data was drawn from a population with distribution dist and alternative hypothesis that it was not.
  • By default a probability value or -value is returned.
  • A small -value suggests that it is unlikely that the data came from dist.
  • The dist can be any symbolic distribution with numeric and symbolic parameters or a dataset.
  • The data can be univariate or multivariate .
  • The KolmogorovSmirnov test assumes that the data came from a continuous distribution.
  • The KolmogorovSmirnov test effectively uses a test statistic based on sup_x TemplateBox[{{{{F, ^, ^}, (, x, )}, -, {F, (, x, )}}}, Abs] where is the empirical CDF of data and is the CDF of dist.
  • For multivariate tests, the sum of the univariate marginal -values is used and is assumed to follow a UniformSumDistribution under .
  • KolmogorovSmirnovTest[data,dist,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • KolmogorovSmirnovTest[data,dist,"property"] can be used to directly give the value of .
  • Properties related to the reporting of test results include:
  • "PValue"-value
    "PValueTable"formatted version of
    "ShortTestConclusion"a short description of the conclusion of a test
    "TestConclusion"a description of the conclusion of a test
    "TestData"test statistic and -value
    "TestDataTable"formatted version of
    "TestStatistic"test statistic
    "TestStatisticTable"formatted
  • The following properties are independent of which test is being performed.
  • Properties related to the data distribution include:
  • "FittedDistribution"fitted distribution of data
    "FittedDistributionParameters"distribution parameters of data
  • The following options can be given:
  • MethodAutomaticthe method to use for computing -values
    SignificanceLevel0.05cutoff for diagnostics and reporting
  • For a test for goodness-of-fit, a cutoff is chosen such that is rejected only if . The value of used for the and properties is controlled by the SignificanceLevel option. By default is set to .
  • With the setting Method->"MonteCarlo", datasets of the same length as the input are generated under using the fitted distribution. The EmpiricalDistribution from KolmogorovSmirnovTest[si,dist,"TestStatistic"] is then used to estimate the -value.
Introduced in 2010
(8.0)