returns the value of .
- 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 "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:
Method Automatic the method to use for computing -values SignificanceLevel 0.05 cutoff 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.
Introduced in 2010