Moments for a ratio of correlated gamma variates

This paper considers the finite integral moments for the ratio, R = X/Y, where X and Y re correlated gamma distributed variables. An analytical and numerical comparison is given for two classes of underlying bivariate gamma distributions. It is shown that the two bivariate gamma structures provide indentical experessions for the mth unadjussted moment, E(R^m), if and only if either of the following conditions hold : 1) X and Y are uncorrelated of 2) m=1. A numerical evaluation is performed to determine the extent that the two methods differ whenever the variables are correlated