Random Number Generation Based on Characteristics Functions

Abstract

Objective: In probability theory and statistics, some distributions can be better presented by the characteristic function (CF) than the conventional probability density function (PDF). In random number generation (RNG) domains, algorithmic applications based on a known CF is far less common compared to the ones that are driven by a density. An acceptance-rejection algorithm that employs CF appeared in the literature in the context of RNG; however, validity, plausibility, and utility of this algorithm have never been examined by a simulation study, which we attempt to address. Material and Methods: We devised a simulation study based on three commonly encountered univariate distributions (Normal, Laplace, and Gamma), and compared the performance of the CF algorithm with the default random number generation tools in R software. Results: All three simulation studies yielded similar outcomes across the two methods with indiscernible differences. Conclusion: The simulation results for the three distributions we considered suggest that the performance of the CF algorithm aligns well with that of the default algorithm. It is better to harness a direct algorithm when the PDF of a random variable is given. However, the CF-based method can offer a solid alternative for situations where the PDF is hard to sample from. Our findings provide a promising basis for conducting further research on generating data in difficult PDF and straightforward CF scenarios. In brief, the CF method is an excellent alternative to the default for generating data when CF is given or can be derived in closed form.