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Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example

Author

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  • Ahmed Nafidi

    (Department of mathematics and informatics, LAMSAD, National School of Applied Sciences of Berrechid, University of Hassan 1, Avenue de l’université, BP 280, Berrechid 26100, Morocco
    These authors contributed equally to this work.)

  • Meriem Bahij

    (Department of mathematics and informatics, LAMSAD, National School of Applied Sciences of Berrechid, University of Hassan 1, Avenue de l’université, BP 280, Berrechid 26100, Morocco
    These authors contributed equally to this work.)

  • Ramón Gutiérrez-Sánchez

    (Department of Statistics and Operational Research, University of Granada, Facultad de Ciencias, Campus de Fuentenueva, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Boujemâa Achchab

    (Department of mathematics and informatics, LAMSAD, National School of Applied Sciences of Berrechid, University of Hassan 1, Avenue de l’université, BP 280, Berrechid 26100, Morocco
    These authors contributed equally to this work.)

Abstract

This paper describes the use of the non-homogeneous stochastic Weibull diffusion process, based on the two-parameter Weibull density function (the trend of which is proportional to the two-parameter Weibull probability density function). The trend function (conditioned and non-conditioned) is analyzed to obtain fits and forecasts for a real data set, taking into account the mean value of the process, the maximum likelihood estimators of the parameters of the model and the computational problems that may arise. To carry out the task, we employ the simulated annealing method for finding the estimators values and achieve the study. Finally, to evaluate the capacity of the model, the study is applied to real modeling data where we discuss the accuracy according to error measures.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:160-:d:312320
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    References listed on IDEAS

    as
    1. 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.
    2. Boumezoued, Alexandre & Hardy, Héloïse Labit & El Karoui, Nicole & Arnold, Séverine, 2018. "Cause-of-death mortality: What can be learned from population dynamics?," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 301-315.
    3. 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.
    4. Boyle, Phelim P. & Freedman, Ruth, 1985. "Population waves and fertility fluctuations: Social security implications," Insurance: Mathematics and Economics, Elsevier, vol. 4(1), pages 65-74, January.
    5. Skvortsov, Alex & Ristic, Branko & Kamenev, Alex, 2018. "Predicting population extinction from early observations of the Lotka–Volterra system," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 371-379.
    6. A. Katsamaki & C. H. Skiadas, 1995. "Analytic solution and estimation of parameters on a stochastic exponential model for a technological diffusion process," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(1), pages 59-75, March.
    7. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2006. "Electricity consumption in Morocco: Stochastic Gompertz diffusion analysis with exogenous factors," Applied Energy, Elsevier, vol. 83(10), pages 1139-1151, October.
    8. 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.
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