Abstract:
The univariate and bivariate central chi-square- and F distributions have received a decent
amount of attention in the literature during the past few decades; the noncentral counterparts
of these distributions have been much less present. This study enriches the existing
literature by proposing bivariate noncentral chi-square and F distributions via the employment
of the compounding method with Poisson probabilities. This method has been
used to a limited extent in the field of distribution theory 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 and
studied, in particular the product, ratio, and proportion. The benefit of introducing
these bivariate noncentral distributions and their respective composites is demonstrated
by graphical representations of their probability density functions. Furthermore, an example
of possible application is given and discussed to illustrate the versatility of the
proposed models.
