Bivariate Beta and Kumaraswamy Models Developed Using the Arnold-Ng Bivariate Beta Distribution

Abstract

In this paper we explore some mechanisms for constructing bivariate and multivariate beta and Kumaraswamy distributions. Specifically, we focus our attention on the Arnold-Ng (2011) eight parameter bivariate beta model. Several models in the literature are identified as special cases of this distribution including the Jones-OlkinLiu-Libby-Novick bivariate beta model, and certain Kotz and Nadarajah bivariate beta models among others. The utility of such models in constructing bivariate Kumaraswamy models is investigated. Structural properties of such derived models are studied. Parameter estimation for the models is also discussed. For illustrative purposes, a real life data set is considered to exhibit the applicability of these models in comparison with rival bivariate beta and Kumaraswamy models.

Keywords

• bivariate beta
• second kind beta distribution
• gamma components
• copulas
• bivariate Kumaraswamy models