The bivariate alpha-skew-normal distribution

ABSTRACT

In this paper, we propose a new bivariate distribution, namely bivariate alpha-skew-normal distribution. The proposed distribution is very flexible and capable of generalizing the univariate alpha-skew-normal distribution as its marginal component distributions; it features a probability density function with up to two modes and has the bivariate normal distribution as a special case. The joint moment generating function as well as the main moments are provided. Inference is based on a usual maximum-likelihood estimation approach. The asymptotic properties of the maximum-likelihood estimates are verified in light of a simulation study. The usefulness of the new model is illustrated in a real benchmark data.

KEYWORDS:

• Alpha-skew-normal distribution
• asymmetry
• bimodality
• bivariate distributions
• skew-normal distribution.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E99

Acknowledgments

The research was sponsored by the Brazilian organizations CNPq, FAPESP, and Serasa-Experian, through their research grant programs.