The Multivariate Skewed Log-Birnbaum–Saunders Distribution and Its Associated Regression Model

Abstract

In this article, a multivariate extension of the unit-sinh-normal (USHN) distribution is presented. The new distribution, which is obtained from the conditionally specified distributions methodology, is absolutely continuous, and its marginal distributions are univariate USHN. The properties of the multivariate USHN distribution are studied in detail, and statistical inference is carried out from a classical approach using the maximum likelihood method. The new multivariate USHN distribution is suitable for modeling bounded data, especially in the (0,1)p region. In addition, the proposed distribution is extended to the case of the regression model and, for the latter, the Fisher information matrix is derived. The numerical results of a small simulation study and two applications with real data sets allow us to conclude that the proposed distribution, as well as its extension to regression models, are potentially useful to analyze the data of proportions, rates, or indices when modeling them jointly considering different degrees of correlation that may exist in the study variables is of interest.