Multivariate Stochastic Rayleigh Process: Computational Aspects, Statistical Inference, Estimation and Prediction Analysis

Yassine Chakroune (), Abdenbi El Azri (), Ahmed Nafidi () and Ilyasse Makroz ()
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Yassine Chakroune: Hassan First University of Settat, National School of Applied Sciences, Laboratory of Systems Modelization and Analysis for Decision Support
Abdenbi El Azri: Hassan First University of Settat, National School of Applied Sciences, Laboratory of Systems Modelization and Analysis for Decision Support
Ahmed Nafidi: Hassan First University of Settat, National School of Applied Sciences, Laboratory of Systems Modelization and Analysis for Decision Support
Ilyasse Makroz: Hassan First University of Settat, National School of Applied Sciences, Laboratory of Systems Modelization and Analysis for Decision Support

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 4, 1-23

Abstract: Abstract The main aim of this paper is to introduce a new multivariate stochastic Rayleigh diffusion process as an extension of the univariate stochastic Rayleigh model, which has been the subject of much research in recent years and to use it to forecast and predict simulated data. Then, we show how the new multivariate model is derived and we present the main distribution properties such as its probability density function, marginal trends and correlation functions. We also study the estimation of the parameters of the created process using a maximum likelihood approach based on time-discrete observations. Otherwise, the simulated data are taken into account and the methodology in question is applied to estimate the parameters. Then, the results obtained are compared with those used in the simulation. Finally, to judge the effectiveness of this process, we will use these statistical results for simulated examples, outlining the possibilities for fitting and prediction.

Keywords: Rayleigh diffusion process; Maximum likelihood estimation; Trend functions; Simulation analysis; Statistical prediction; 62M86; 60H30; 65C30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10223-0

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