The alpha–beta skew normal distribution: properties and applications

Abstract

This paper introduces a new class of skew distributions by extending the alpha skew normal distribution proposed by Elal-Olivero [Elal-Olivero, D. Alpha-skew-normal distribution. Proyecciones. 2010;29:224–240]. Statistical properties of the new family are studied in details. In particular, explicit expressions for the moments and the shape parameters including the skewness and the kurtosis coefficients and the moment generating function are derived. The problem of estimating parameters on the basis of a random sample coming from the new class of distribution is considered. To examine the performance of the obtained estimators, a Monte Carlo simulation study is conducted. Flexibility and usefulness of the proposed family of distributions are illustrated by analysing three real data sets.

Keywords:

• information matrix
• maximum likelihood estimation
• moment generating function
• skewness

Acknowledgements

The authors are grateful to the Editor-in-Chief, the Associate Editor and anonymous referees for their many helpful comments and suggestions on an earlier version of this paper which led to this improved version.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by a grant from Ferdowsi University of Mashhad (No MS94330DSP).