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

• Published in: Journal of statistical computation and simulation Vol. 89; no. 17; pp. 3258 - 3272
• Main Authors: González-Estrada, Elizabeth, Cosmes, Waldenia
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 22-11-2019; Taylor & Francis Ltd
• Subjects: 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
• DOI: 10.1080/00949655.2019.1658763

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.