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

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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
    Faculty of Sciences, Ibn Tofail University, Laboratory of Analysis, Geometry and Applications (LAGA))

  • Abdenbi El Azri

    (Hassan First University of Settat, National School of Applied Sciences, Laboratory of Systems Modelization and Analysis for Decision Support
    Higher Institute of Nursing Professions and Techniques of Health ISPITS Casablanca)

  • 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)

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.

Suggested Citation

  • Yassine Chakroune & Abdenbi El Azri & Ahmed Nafidi & Ilyasse Makroz, 2025. "Multivariate Stochastic Rayleigh Process: Computational Aspects, Statistical Inference, Estimation and Prediction Analysis," Methodology and Computing in Applied Probability, Springer, vol. 27(4), pages 1-23, December.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:4:d:10.1007_s11009-025-10223-0
    DOI: 10.1007/s11009-025-10223-0
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