Extremely efficient generation of Gamma random variables for \alpha >= 1

TL;DR

This paper introduces a highly efficient accept/reject algorithm for generating independent Gamma random variables with shape parameter   , outperforming existing methods especially for    and approaching perfect acceptance as  increases.

Contribution

The paper presents a novel accept/reject algorithm that significantly improves the efficiency of generating Gamma variables for   , especially for larger .

Findings

Higher acceptance rates than existing methods for   .

Acceptance rate approaches 1 as  increases.

Method is simple and suitable for signal processing applications.

Abstract

The Gamma distribution is well-known and widely used in many signal processing and communications applications. In this letter, a simple and extremely efficient accept/reject algorithm is introduced for the generation of independent random variables from a Gamma distribution with any shape parameter \alpha >= 1. The proposed method uses another Gamma distribution with integer \alpha_p <= \alpha, from which samples can be easily drawn, as proposal function. For this reason, the new technique attains a higher acceptance rate (AR) for \alpha >= 3 than all the methods currently available in the literature, with AR tends to 1 as \alpha\ diverges.