Bayesian approach to epsilon-skew-normal family

ABSTRACT

The estimation problem of epsilon-skew-normal (ESN) distribution parameters is considered within Bayesian approaches. This family of distributions contains the normal distribution, can be used for analyzing the asymmetric and near-normal data. Bayesian estimates under informative and non informative Jeffreys prior distributions are obtained and performances of ESN family and these estimates are shown via a simulation study. A real data set is also used to illustrate the ideas.

KEYWORDS:

• Bayes estimates
• Epsilon skew normal
• Frequentist risk
• Jeffreys prior
• Skewness

Acknowledgments

The authors would like to thank the anonymous reviewers for their suggestions, corrections and encouragement, which helped us to improve the earlier versions of the manuscript. We would like to thank Professor Reinaldo Boris Arellano Valle for insightful comments. We gratefully acknowledge the support of this work by Shiraz University Research Council.