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

returns the value of .

Details and OptionsDetails and Options

  • MardiaCombinedTest performs a 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 combined test effectively pools the results from MardiaSkewnessTest and MardiaKurtosisTest.
  • MardiaCombinedTest[data,dist,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • MardiaCombinedTest[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 .
  • With the setting Method->"MonteCarlo", datasets of the same length as the input are generated under using the fitted distribution. The EmpiricalDistribution from MardiaCombinedTest[si,"TestStatistic"] is then used to estimate the -value.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Perform a test for multivariate normality:

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Click for copyable input
Click for copyable input

Extract the test statistic from the Mardia combined test:

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Click for copyable input

Obtain a formatted test table:

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Click for copyable input
Introduced in 2010
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