Some bivariate and multivariate families of distributions: Theory, inference and application

Abstract

The bivariate and multivariate probability distributions are useful in joint modeling of several random variables. The development of bivariate and multivariate distributions is relatively tedious as compared with the development of univariate distributions. In this paper we have proposed a new method of developing bivariate and multivariate families of distributions from the univariate marginals. The properties of the proposed families of distributions have been studies. These properties include marginal and conditional distributions; product, ratio and conditional moments; joint reliability function and dependence measures. Statistical inference about the proposed families of distributions has also been done. The proposed bivariate family of distributions has been studied for Weibull baseline distribution giving rise to a new bivariate Weibull distribution. The properties of the proposed bivariate Weibull distribution have been studied alongside maximum likelihood estimation of the unknown parameters. The proposed bivariate Weibull distribution has been used for modeling of real bivariate data sets and we have found that the proposed bivariate Weibull distribution has been a suitable choice for the modeling of data used.

Keywords

• bivariate distributions
• t-x family of distributions
• transmuted distributions
• weibull distribution
• dependence measures
• maximum likelihood estimation