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Generalized skew normal model. (English) Zbl 1076.62096
Summary: The skew normal distribution proposed by A. A. Azzalini [Scand. J. Stat., Theory Appl. 12, 171–178 (1985; Zbl 0581.62014)] can be a suitable model for the analysis of data exhibiting a unimodal density function having some skewness present, a structure often occurring in data analysis. We study a generalization of the basic Azzalini model proposed by Balakrishnan, as a discussant of B. C. Arnold and R. J. Beaver [Test 11, 7–54 (2002; Zbl 1033.62013)]. The basic structural properties of the model including the reliability properties are presented. Estimation and testing of hypothesis of the skew parameter are discussed. Some comparisons of the models in terms of mean, variance and skewness are provided. Two data sets are analyzed.

MSC:
62N02 Estimation in survival analysis and censored data
60E15 Inequalities; stochastic orderings
62E15 Exact distribution theory in statistics
62N05 Reliability and life testing
62F03 Parametric hypothesis testing
62F10 Point estimation
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