A New Method of Generating Truncated Bivariate Families of Distributions

Abstract

The modeling of complex data has attracted several researchers for the quest of generating new probability distributions. The joint modeling of two variables asks for some additional complexities as a bivariate distribution is needed. The field of research in developing bivariate families of distributions is somewhat new. In certain situations, the domain of data is restricted and some truncated distribution is required. Several univariate truncated families of distributions are available for modeling of a single variable but the bivariate truncated families of distributions has not been studied and in this paper, we have proposed a new bivariate truncated families of distributions. A specific sub-family has been proposed by using the bivariate Burr as a base-line distribution, resulting in a bivariate truncated Burr family of distributions. Some important statistical properties of the proposed family has been studied, which include the marginal and conditional distributions, bivariate reliability, and bivariate hazard rate functions. The maximum likelihood estimation for the parameters of the family is also carried out. The proposed bivariate truncated Burr family of distributions is studied for the Burr baseline distributions, giving rise to the bivariate truncated Burr-Burr distribution. The new bivariate truncated Burr-Burr distribution is explored in detail and several statistical properties of the new distribution are studied, which include the marginal and conditional distributions, product, ratio, and conditional moments. The maximum likelihood estimation for the parameters of the proposed distribution is done. The proposed bivariate truncated Burr-Burr distribution is used to model some real data sets. It is found that the proposed distribution performs better than the other distributions considered in this study.