A New Class of Bivariate Distributions: Properties, Estimation, and Modeling

The development of bivariate distributions is a challenging area of research, and a novel class of bivariate distributions is proposed in this paper. Certain useful mathematical characteristics of the proposed class of bivariate distributions are explored in general. These properties include the joint and conditional and joint survival function moments and measures of dependence. The parameters of the proposed class of distributions are estimated using the maximum likelihood method of estimation. A multivariate version of the proposed class is also proposed, and some necessary properties are discussed. The multivariate dependence measures are obtained for the proposed multivariate class of distributions. A new bivariate power function distribution is proposed using the power function distribution as a baseline distribution in the proposed bivariate class. Some useful properties of the proposed bivariate distribution are studied. The parameters of the proposed bivariate distribution are estimated using the maximum likelihood method. An extensive simulation study has been conducted to see the performance of the estimation method. The new bivariate power function distribution is used to model some real data.