This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# JarqueBeraALMTest

 JarqueBeraALMTest[data] tests whether data is normally distributed using the Jarque-Bera ALM test. JarqueBeraALMTest returns the value of .
• JarqueBeraALMTest performs the Jarque-Bera ALM goodness-of-fit test with null hypothesis that data was drawn from a NormalDistribution 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 dist can be any symbolic distribution with numeric and symbolic parameters or a dataset.
• The data can be univariate or multivariate .
• The Jarque-Bera ALM test effectively compares the skewness and kurtosis of data to a NormalDistribution.
• For univariate data the test statistic is given by with , and correction factors for finite sample sizes given by , , and .
• For multivariate tests, the mean of the univariate marginal test statistics is used. -values are computed via Monte Carlo simulation.
• Properties related to the reporting of test results include:
 "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 .
Perform a Jarque-Bera ALM test for normality:
Perform a test for multivariate normality:
Extract the test statistic from a Jarque-Bera ALM test:
Perform a Jarque-Bera ALM test for normality:
 Out[2]=

Perform a test for multivariate normality:
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Extract the test statistic from a Jarque-Bera ALM test:
 Out[2]=
 Scope   (6)
Perform a Jarque-Bera ALM test for normality:
The -value for the normal data is large compared to the -value for the non-normal data:
Test for multivariate normality:
Create a HypothesisTestData object for repeated property extraction:
The properties available for extraction:
Tabulate the results of the Jarque-Bera ALM test:
The full test table:
A -value table:
The test statistic:
Retrieve the entries from a Jarque-Bera ALM test table for custom reporting:
Report test conclusions using and :
The conclusion may differ at a different significance level:
 Options   (3)
Use Monte Carlo-based methods or a computation formula:
Set the number of samples to use for Monte Carlo-based methods:
The Monte Carlo estimate converges to the true -value with increasing samples:
Set the random seed used in Monte Carlo-based methods:
The seed affects the state of the generator and has some effect on the resulting -value:
 Applications   (2)
A power curve for the Jarque-Bera ALM test:
Visualize the approximate power curve:
Estimate the power of the Jarque-Bera ALM test when the underlying distribution is a CauchyDistribution, the test size is 0.05, and the sample size is 12:
Create a Jarque-Bera ALM test statistic generalized for other distributions:
Finite-sample values for , , and :
A Jarque-Bera ALM test statistic for fitting to a LaplaceDistribution:
Perform the generalized test on some data:
The -values are uniform as expected:
The test is powerful against the alternative of a HyperbolicDistribution of similar mean and variance: