Gamma Pseudo Random Number Generators

Abstract

The generation of random values corresponding to an underlying Gamma distribution is a key capability in many areas of knowledge, such as Probability and Statistics, Signal Processing, or Digital Communication, among others. Throughout history, different algorithms have been developed for the generation of such values and advances in computing have made them increasingly faster and more efficient from a computational point of view. These advances also allow the generation of higher-quality inputs (from the point of view of randomness and uniformity) for these algorithms that are easily tested by different statistical batteries such as NIST, Dieharder, or TestU01 among others. This article describes the existing algorithms for the generation of (independent and identically distributed—i.i.d.) Gamma distribution values as well as the theoretical and mathematical foundations that support their validity.