Title: Enhanced Box-Muller method for high quality Gaussian random number generation

Authors: Adnane Addaim; Driss Gretete; Abdessalam Ait Madi

Addresses: National School of Applied Sciences (ENSA), Ibn Tofail University, B.P 241, Compus Universitaire, 14000, Kenitra, Morocco ' National School of Applied Sciences (ENSA), Ibn Tofail University, B.P 241, Compus Universitaire, 14000, Kenitra, Morocco ' National School of Applied Sciences (ENSA), Ibn Tofail University, B.P 241, Compus Universitaire, 14000, Kenitra, Morocco

Abstract: Fast and high-quality Gaussian random number generation (GRNG) is a key capability for simulations across a wide range of disciplines. In this article, we present an enhanced Box-Muller method for GRNG using one uniform variable. Its probability density function (PDF) is given in closed form as a function of one parameter. In this article, the theoretical basis of this method is quite thoroughly discussed and is evaluated using several different statistical tests, including the chi-square test and the Anderson-Darling test. The simulations results show good performances of this method which generates accurately a true Gaussian PDF even at very high σ (standard deviations) values in comparison with the standard Box-Muller method.

Keywords: Gaussian random number generation; GRNG; Box-Muller method; statistical tests.

DOI: 10.1504/IJCSM.2018.093153

International Journal of Computing Science and Mathematics, 2018 Vol.9 No.3, pp.287 - 297

Received: 06 May 2017
Accepted: 19 Jun 2017

Published online: 29 Jun 2018 *

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