Chaotic Method for Generating q-Gaussian Random Variables

This study proposes a pseudorandom number generator of
$q$
-Gaussian random variables for a range of
$q$
values,
$-\infty < q < 3$
, 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.