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BUILT-IN MATHEMATICA SYMBOL
MardiaKurtosisTest
MardiaKurtosisTest[data]
tests whether data follows a MultinormalDistribution using the Mardia kurtosis test.
MardiaKurtosisTest[data, "property"]
returns the value of 
.
Details 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 "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 
-valuesSignificanceLevel 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 
. - The following methods can be used to compute
-values: -
Automatic correct 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.
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