Density and Distribution Evaluation for Convolution of Independent Gamma Variables

TL;DR

This paper compares various numerical methods for evaluating the density and distribution of convoluted independent gamma variables and introduces an efficient formula for renewal process event counts.

Contribution

It provides a comparative analysis of numerical techniques and derives a new efficient formula for gamma convolutions in renewal processes.

Findings

Numerical methods vary in accuracy and speed.

The new formula improves efficiency in renewal process calculations.

Comparative results guide method selection for gamma convolutions.

Abstract

Several numerical evaluations of the density and distribution of convolution of independent gamma variables are compared in their accuracy and speed. In application to renewal processes, an efficient formula is derived for the probability mass function of the event count.