Some bivariate gamma distributions

We introduce two new bivariate gamma distributions based on a characterizing property involving products of gamma and beta random variables. We derive various representations for their joint densities, product moments, conditional densities and conditional moments. Some of these representations involve special functions such as the complementary incomplete gamma and Whittaker functions. We also discuss ways to construct multivariate generalizations. (C) 2005 Elsevier Ltd. All rights reserved.