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Shapiro-Wilk test for skew normal distributions based on data transformations. (English) Zbl 07193895

Summary: 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.

MSC:

62G10 Nonparametric hypothesis testing
62F40 Bootstrap, jackknife and other resampling methods
62E10 Characterization and structure theory of statistical distributions

Software:

sn; R; findGSE
PDFBibTeX XMLCite
Full Text: DOI

References:

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