Bivariate noncentral distributions: An approach via the compounding method

Abstract

This paper enriches the existing literature of bivariate noncentral distributions by proposing bivariate noncentral generalised chi-square and F distributions via the employment of the compounding method with Poisson probabilities. This method has been used to a limited extent to obtain univariate noncentral distributions; this study extends some results in literature to the corresponding bivariate setting. The process which is followed to obtain such bivariate noncentral distributions is systematically described and motivated. Some distributions of composites (univariate functions of the dependent components of the bivariate distributions) are derived, in particular the product, ratio, and proportion. Furthermore, an example of possible application is given and discussed to illustrate the versatility of the proposed models.