A note on the correlated gamma distribution of Loaiciga and Leipnik

The recent paper by Loaiciga and Leipnik [Loaiciga HA, Leipnik RB. Correlated gamma variables in the analysis of microbial densities in water. Adv Water Resour 2005;28:329–35] introduced a novel bivariate gamma distribution and studied its ratio distribution with application to hydrological sciences. In this note, we derive the corresponding distributions of the sum and the product. We also derive a powerful mixture representation of the bivariate gamma distribution unnoticed by Loaiciga and Leipnik.