Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

BaringhausHenzeTest

BaringhausHenzeTest[data]
tests whether data follows a MultinormalDistribution using the BaringhausHenze test.

BaringhausHenzeTest[data,MultinormalDistribution[μ,Σ]]
tests whether data follows the distribution with mean vector μ and covariance matrix Σ.

BaringhausHenzeTest[data,"property"]
returns the value of "property".

Details and OptionsDetails 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:
•  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 "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. »

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Perform a test for multivariate normality:

 In[1]:=
 In[2]:=
 Out[2]=

Extract the test statistic from the BaringhausHenze test:

 In[1]:=
 In[2]:=
 Out[2]=

Obtain a formatted test table:

 In[1]:=
 In[2]:=
 Out[2]=

Neat Examples  (1)Neat Examples  (1)

Introduced in 2015
(10.2)