tests whether data follows a MultinormalDistribution using the Mardia kurtosis test.

returns the value of .

Details and OptionsDetails and Options

  • MardiaKurtosisTest performs the Mardia kurtosis goodness-of-fit test with null hypothesis that data was drawn from a MultinormalDistribution 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 data can be univariate or multivariate .
  • The Mardia kurtosis test effectively compares a multivariate measure of kurtosis for data to a MultinormalDistribution.
  • MardiaKurtosisTest[data,dist,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • MardiaKurtosisTest[data,dist,"property"] can be used to directly give the value of .
  • PearsonChiSquareTest[data,dist,"property"] can be used to directly give the value of .
  • Properties related to the reporting of test results include:
  • "DegreesOfFreedom"the degrees of freedom used in a test
    "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
  • 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 .
  • The following methods can be used to compute -values:
  • Automaticcorrect for small samples up to dimension 5
    "Asymptotic"use the asymptotic distribution of the test statistic
    "MonteCarlo"use Monte Carlo simulation
  • With the setting Method-> "MonteCarlo", datasets of the same length as the input are generated under using the fitted distribution. The EmpiricalDistribution from MardiaKurtosisTest[si,"TestStatistic"] is then used to estimate the -value.
Introduced in 2010