On the density for sums of independent exponential, Erlang and gamma variates

Abstract

This paper re-examines the density for sums of independent exponential, Erlang and gamma random variables. By using a divided difference perspective, the paper provides a unified approach to finding closed-form formulae for such convolutions. In particular, the divided difference perspective for sums of Erlang variates suggests a new approach to finding the density for sums of independent gamma variates using fractional calculus.