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The stochastic Weibull diffusion process: Computational aspects and simulation

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  • Nafidi, A.
  • Bahij, M.
  • Achchab, B.
  • Gutiérrez-Sanchez, R.

Abstract

This paper presents a new stochastic diffusion process, in which the mean function is proportional to the density function of the Weibull distribution. This is considered a useful model for survival populations, reliability studies and life-testing experiments. The main features of the process are analysed, including the transition probability density function and conditional and non-conditional mean functions. The parameters of the process are estimated by maximum likelihood using discrete sampling. Newton-Raphson and simulated annealing numerical methods are proposed to solve the likelihood equations, and are compared using a simulation example.

Suggested Citation

  • Nafidi, A. & Bahij, M. & Achchab, B. & Gutiérrez-Sanchez, R., 2019. "The stochastic Weibull diffusion process: Computational aspects and simulation," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 575-587.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:575-587
    DOI: 10.1016/j.amc.2018.12.017
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    References listed on IDEAS

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    1. Nafidi, A. & Gutiérrez, R. & Gutiérrez-Sánchez, R. & Ramos-Ábalos, E. & El Hachimi, S., 2016. "Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors," Energy, Elsevier, vol. 113(C), pages 309-318.
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    4. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2009. "The trend of the total stock of the private car-petrol in Spain: Stochastic modelling using a new gamma diffusion process," Applied Energy, Elsevier, vol. 86(1), pages 18-24, January.
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    7. 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 & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez, 2019. "Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    2. 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.
    3. Nafidi, Ahmed & El Azri, Abdenbi, 2021. "A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 25-38.

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