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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Vydané v:Journal of statistical computation and simulation Ročník 89; číslo 17; s. 3258 - 3272
Hlavní autori: González-Estrada, Elizabeth, Cosmes, Waldenia
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Abingdon Taylor & Francis 22.11.2019
Taylor & Francis Ltd
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Abstract 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.
AbstractList 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.
Author Cosmes, Waldenia
González-Estrada, Elizabeth
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  surname: Cosmes
  fullname: Cosmes, Waldenia
  organization: Colegio de Postgraduados
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Snippet 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...
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SubjectTerms 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
Title Shapiro-Wilk test for skew normal distributions based on data transformations
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