Skewed Multivariate Birnbaum-Saunders Distributions

TL;DR

This paper introduces a skewed multivariate Birnbaum-Saunders distribution, extending the univariate model to handle multivariate data with skewness, and demonstrates its properties, estimation methods, and practical application.

Contribution

It defines a new skewed multivariate Birnbaum-Saunders distribution with derived properties and estimation techniques, including a bivariate extension and real data application.

Findings

Distribution has univariate Birnbaum-Saunders marginals

Maximum likelihood estimation is feasible and Fisher information is derived

Application to real data shows practical usefulness

Abstract

The univariate Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this article, we define a skewed version of the Birnbaum-Saunders distribution in the multivariate setting and derive several of its properties. The proposed skewed multivariate model is an absolutely continuous distribution whose marginals are univariate Birnbaum-Saunders distributions. Estimation of the parameters by maximum likelihood is discussed and the Fisher's information matrix is determined. A skewed bivariate version for the generalized Birnbaum-Saunders distribution is also introduced. We provide an application to real data which illustrates the usefulness of the proposed multivariate model.