JarqueBeraALMTest

JarqueBeraALMTest[data]

tests whether data is normally distributed using the JarqueBera ALM test.

JarqueBeraALMTest[data,"property"]

returns the value of "property".

Details and Options

  • JarqueBeraALMTest performs the JarqueBera 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 is normally distributed.
  • The data can be univariate {x1,x2,} or multivariate {{x1,y1,},{x2,y2,},}.
  • The JarqueBera ALM test effectively compares the skewness and kurtosis of data to a NormalDistribution.
  • For univariate data, the test statistic is given by with b_1=Skewness[data], b_2=Kurtosis[data] and correction factors for finite sample sizes given by , , and .
  • For multivariate tests, the sum of the univariate marginal -values is used and is assumed to follow a UniformSumDistribution under .
  • JarqueBeraALMTest[data,dist,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • JarqueBeraALMTest[data,dist,"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", datasets of the same length as the input are generated under using the fitted distribution. The EmpiricalDistribution from JarqueBeraALMTest[si,"TestStatistic"] is then used to estimate the -value.

Examples

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Basic Examples  (3)

Perform a JarqueBera ALM test for normality:

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Perform a test for multivariate normality:

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Extract the test statistic from a JarqueBera ALM test:

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Scope  (6)

Options  (3)

Applications  (2)

Properties & Relations  (4)

Possible Issues  (1)

Neat Examples  (1)

See Also

HypothesisTestData  AndersonDarlingTest  KolmogorovSmirnovTest  CramerVonMisesTest  DistributionFitTest  KuiperTest  MardiaCombinedTest  MardiaKurtosisTest  MardiaSkewnessTest  PearsonChiSquareTest  ShapiroWilkTest  WatsonUSquareTest

Introduced in 2010
(8.0)