Abstract
Applying the theory on multiple hypergeometric functions, the distribution of a weighted convolution of gamma variables is characterized through explicit forms for the probability density function, the distribution function and the moments about the origin. The main results unify some previous contributions in the literature on finite convolution of gamma distributions. We deal with computational aspects that arise from the representations in terms of multiple hypergeometric functions, introducing a new integral representation for the fourth Lauricella function and its confluent form
, suitable for numerical integration; some graphics of the probability density function and distribution function show that the proposed numerical approach supply good estimates for the special functions involved. We briefly outline two interesting applications of special function theory in statistics: the weighted convolutions of gamma matrices random variables and the weighted convolutions of gamma variables with random weights.
Acknowledgements
I wish to thank Professor Gianfranco Lovison for many suggestions and careful reading of the paper.