Information geometry for testing pseudorandom number generators

TL;DR

This paper introduces an information geometric approach to evaluate pseudorandom number generators by analyzing the gamma distribution manifold, demonstrated with Mathematica, offering a new tool for testing randomness in finite samples.

Contribution

It presents a novel geometric framework for testing pseudorandom generators based on gamma distribution manifolds, expanding current testing methodologies.

Findings

The geometric approach can distinguish different pseudorandom generators.

Application to Mathematica's generator demonstrates practical utility.

Potential to enhance existing randomness testing procedures.

Abstract

The information geometry of the 2-manifold of gamma probability density functions provides a framework in which pseudorandom number generators may be evaluated using a neighbourhood of the curve of exponential density functions. The process is illustrated using the pseudorandom number generator in Mathematica. This methodology may be useful to add to the current family of test procedures in real applications to finite sampling data.