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Trend analysis and computational statistical estimation in a stochastic Rayleigh model: Simulation and application

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  • Gutiérrez, R.
  • Gutiérrez-Sánchez, R.
  • Nafidi, A.

Abstract

This paper considers a stochastic model based on the homogeneous stochastic Rayleigh diffusion process. We first examine the main probabilistic characteristics of the model and describe, among other results, an explicit expression of the trends (both conditioned and nonconditioned) and, when it exists, the stationary distribution. We then obtain results of the statistical estimation of the corresponding parameters and consider the computational problems that may arise. In addition, we present an algorithm for the stochastic simulation of the sample path of the model based on the corresponding Ito stochastic differential equation. Finally, the model is applied to study the evolution of the production of thermal electricity in countries in the Maghreb region; the results obtained are in good statistical accord with the real data observed for the period 1980–2002.

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  • Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2008. "Trend analysis and computational statistical estimation in a stochastic Rayleigh model: Simulation and application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 209-217.
    • Handle: RePEc:eee:matcom:v:77:y:2008:i:2:p:209-217
    DOI: 10.1016/j.matcom.2007.08.017
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    References listed on IDEAS

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    1. L. Ferrante & S. Bompadre & L. Possati & L. Leone, 2000. "Parameter Estimation in a Gompertzian Stochastic Model for Tumor Growth," Biometrics, The International Biometric Society, vol. 56(4), pages 1076-1081, December.
    2. Ramón Gutiérrez & Patrica Román & Francisco Torres, 2001. "Inference on some parametric functions in the univeriate lognormal diffusion process with exogenous factors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 357-373, December.
    3. Guerra, Maria Letizia & Stefanini, Luciano, 2000. "A comparative simulation study for estimating diffusion coefficient," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(3), pages 193-203.
    4. Gutiérrez, R. & Nafidi, A. & Gutiérrez Sánchez, R., 2005. "Forecasting total natural-gas consumption in Spain by using the stochastic Gompertz innovation diffusion model," Applied Energy, Elsevier, vol. 80(2), pages 115-124, February.
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    Cited by:

    1. Ahmed Nafidi & Meriem Bahij & Ramón Gutiérrez-Sánchez & Boujemâa Achchab, 2020. "Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example," Mathematics, MDPI, vol. 8(2), pages 1-11, January.
    2. Gutiérrez-Sánchez, R. & Nafidi, A. & Pascual, A. & Ramos-Ábalos, E., 2011. "Three parameter gamma-type growth curve, using a stochastic gamma diffusion model: Computational statistical aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 234-243.
    3. Nenghui Kuang & Huantian Xie, 2013. "Large and moderate deviations in testing Rayleigh diffusion model," Statistical Papers, Springer, vol. 54(3), pages 591-603, August.

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