Parameters estimation of the Rayleigh diffusion process: Inference aspects and application to real data

Chakroune Yassine (), Nafidi Ahmed () and El Azri Abdenbi ()
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Chakroune Yassine: Department of Mathematics and Computer Science, Laboratory of Systems Modelization and Analysis for Decision Support, National School of Applied Science, Hassan First University of Settat, B. P. 218, 26103 Berrechid, Morocco
Nafidi Ahmed: Department of Mathematics and Computer Science, Laboratory of Systems Modelization and Analysis for Decision Support, National School of Applied Science, Hassan First University of Settat, B. P. 218, 26103 Berrechid, Morocco
El Azri Abdenbi: Higher Institute of Nursing Professions and Techniques of Health ISPITS Casablanca, Rue Mohamed Al Fidouzi, 20250 Casablanca, Morocco

Monte Carlo Methods and Applications, 2025, vol. 31, issue 3, 247-255

Abstract: In this paper, a stochastic model related to the Rayleigh density function curve is proposed. First, we determined the explicit form of the process by solving the stochastic differential equation by applying the Itô method. Then we determined the probabilistic characteristics such as the density function, the mean and the conditional mean functions. Unlike other processes in the same context, this one allowed us to find the explicit form of the estimators of these parameters by solving the maximum likelihood equations system. In addition, an estimation study on simulated data is carried out in order to validate the efficiency of the estimators proposed by the maximum likelihood methodology. Finally, an application to real data is presented.

Keywords: Rayleigh density function; maximum likelihood; computational estimation; electricity production; oil sources (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/mcma-2025-2014

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