Weibull-like bivariate probability density function and associated estimation algorithms

Abstract

We propose to introduce a new class of bivariate probability distributions, which we believe is of great interest to statisticians and data scientists. However different from the conventional Weibull it might be, the density function posited herein allows to generalize its properties in two dimensions (2D). This new function, essentially, has structure characteristics and properties different from those of the various bivariate Weibull-type functions found in the literature. The main features, such as the marginal distributions, moments, characteristic functions of this bivariate density are defined. Two related maximum likelihood estimation algorithms are also explicated, tested, and compared. Numerical simulations show the practicality of these algorithms as well as the interest of the new density in several areas of data analysis and extreme values modeling.