tests whether data follows a MultinormalDistribution using the BaringhausHenze test.


tests whether data follows the distribution with mean vector μ and covariance matrix Σ.


returns the value of "property".

Details and Options

  • BaringhausHenzeTest performs a goodness-of-fit test, with null hypothesis that data was drawn from a MultinormalDistribution and alternative hypothesis that it was not.
  • BaringhausHenzeTest is also known as BaringhausHenzeEppsPulley multivariate normality test, or BHEP test.
  • By default, a probability value or -value is returned.
  • A small -value suggests that it is unlikely that the data came from a multivariate normal distribution.
  • The data can be univariate {x1,,xn} or multivariate {{x1,y1,},,{xn,yn,}}.
  • The BaringhausHenze test effectively uses a test statistic Tβ based on an distance between the empirical characteristic function of decorrelated standardized data and the standard multivariate Gaussian characteristic function Tβ=Expectation[n Abs[Ψemp[t]-Ψst[t]]2,{t1,,td}], where =ProductDistribution[{NormalDistribution[0,β],d}]. »
  • The β parameter is positive and determines the smoothing of the empirical distribution. It is automatically determined, but can be changed using a Method setting.
  • BaringhausHenzeTest[data,MultinormalDistribution[μ,Σ],"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • BaringhausHenzeTest[data,MultinormalDistribution[μ,Σ],"property"] can be used to directly give the value of "property".
  • Properties related to the reporting of test results include:
  • "PValue"-value
    "PValueTable"formatted version of "PValue"
    "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 "TestData"
    "TestStatistic"test statistic
    "TestStatisticTable"formatted "TestStatistic"
  • 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 "TestConclusion" and "ShortTestConclusion" properties is controlled by the SignificanceLevel option. By default, is set to 0.05. »
  • With the setting Method->"MonteCarlo", a number of datasets of the same length as the input are generated under using the fitted distribution. The EmpiricalDistribution from BaringhausHenzeTest[si,"TestStatistic"] is then used to estimate the -value. »
  • The setting Method{method,"SmoothingParameter"β} allows for a custom smoothing parameter β. By default, , in which case the test is also known as the HenzeZirkler test. »


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Basic Examples  (3)

Perform a test for multivariate normality:

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Extract the test statistic from the BaringhausHenze test:

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Obtain a formatted test table:

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Scope  (6)

Options  (3)

Applications  (4)

Properties & Relations  (5)

Neat Examples  (1)

Introduced in 2015