On the Ratio X/y for The

For a bivariate random vector (X, Y), the distribution of the ratio X/Y is of interest in problems in biological and physical sciences, econometrics, and ranking and selection. Examples include Mendelian inheritance ratios in genetics, mass to energy ratios in nuclear physics, target to control precipitation in meteorology, and inventory ratios in economics. The distribution of X/Y has been studied by several authors especially when X and Y are independent random variables and come from the same family. For instance, see Marsaglia [1] and Korhonen and Narula [2] for normal family, Press [3] for Student's t family, Basu and Lochner [4] for Weibull family, Shcolnick [5] for stable family, Hawkins and Han [6] for non-central chisquared family, and Provost [7] for gamma family. However, there is relatively little work of this kind when X and Y are correlated random variables. Some of the known work include Hinkley [8] for bivariate normal family, Kappenman [9] for bivariate t family, and Lee et al [10] for bivariate gamma family. In this paper, we study the distribution of X/Y when (X, Y) has the elliptically symmetric Bessel distribution given by the joint probability density function (pdf)