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Bayesian inference for the skewness parameter of the scalar skew-normal distribution. (English) Zbl 1319.62057

Summary: The skew-normal distribution includes the normal distribution as a special case. This family of distributions has a shape parameter that defines the direction of the asymmetry of the distribution, also called skewness parameter. The main focus of this paper will be showing that the Bayesian approach using MCMC methods is a good alternative to make inference under the skewness parameter. We present a brief discuss about prior choice and propose an approximation for the Jeffreys prior developed by B. Liseo and N. Loperfido [J. Stat. Plann. Inference 136, No. 2, 373–389 (2006; Zbl 1077.62017)]. We also provide an approximation for the bias correction factor proposed by N. Sartori [J. Stat. Plann. Inference 136, No. 12, 4259–4275 (2006; Zbl 1098.62023)]. A simulation study is presented to compare the bias, mean square error and interval estimates using the maximum likelihood and different Bayes estimators. Finally, hypotheses tests are considered using Bayes factor and the likelihood ratio test.

MSC:

62F15 Bayesian inference
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