Chaotic Method for Generating q-Gaussian Random Variables

TL;DR

This paper introduces a novel chaotic map-based pseudo random number generator for q-Gaussian variables, effectively producing samples that pass standard statistical tests across a broad range of q values.

Contribution

It presents a new deterministic chaotic map method for generating q-Gaussian random variables applicable for various q values, validated by statistical testing.

Findings

Generated samples pass KS test for q in -1.0 to 2.7

Samples pass AD test for q in -1 to 2.4

Method works across a wide q range with statistical validation

Abstract

This study proposes a pseudo random number generator of q-Gaussian random variables for a range of q values, -infinity < q < 3, based on deterministic chaotic map dynamics. Our method consists of chaotic maps on the unit circle and map dynamics based on the piecewise linear map. We perform the q-Gaussian random number generator for several values of q and conduct both Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) tests. The q-Gaussian samples generated by our proposed method pass the KS test at more than 5% significance level for values of q ranging from -1.0 to 2.7, while they pass the AD test at more than 5% significance level for q ranging from -1 to 2.4.