Shapiro-Wilk test for skew normal distributions based on data transformations

A probability property that connects the skew normal (SN) distribution with the normal distribution is used for proposing a goodness-of-fit test for the composite null hypothesis that a random sample follows an SN distribution with unknown parameters. The random sample is transformed to approximatel...

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Veröffentlicht in:Journal of statistical computation and simulation Jg. 89; H. 17; S. 3258 - 3272
Hauptverfasser: González-Estrada, Elizabeth, Cosmes, Waldenia
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Taylor & Francis 22.11.2019
Taylor & Francis Ltd
Schlagworte:
Anderson-Darling test
Computer simulation
Goodness of fit
Monte Carlo simulation
Normal distribution
Normality
normality test
Null hypothesis
Parameters
parametric bootstrap
Random variables
skew data sets
Skewed distributions
Statistical analysis
Statistical tests
tests of hypotheses
ISSN:0094-9655, 1563-5163
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Zusammenfassung:A probability property that connects the skew normal (SN) distribution with the normal distribution is used for proposing a goodness-of-fit test for the composite null hypothesis that a random sample follows an SN distribution with unknown parameters. The random sample is transformed to approximately normal random variables, and then the Shapiro-Wilk test is used for testing normality. The implementation of this test does not require neither parametric bootstrap nor the use of tables for different values of the slant parameter. An additional test for the same problem, based on a property that relates the gamma and SN distributions, is also introduced. The results of a power study conducted by the Monte Carlo simulation show some good properties of the proposed tests in comparison to existing tests for the same problem.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2019.1658763