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Open AccessArticle

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

1
Univ. Hassan 1, LAMSAD, École Nationale des Sciences Appliquées de Berrechid, Avenue de l’université, BP 280, Berrechid 26100, Morocco
2
Department of Statistics and Operational Research, University of Granada, Facultad de Ciencias, Campus de Fuentenueva, 18071 Granada, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(2), 160; https://doi.org/10.3390/math8020160
Received: 10 December 2019 / Revised: 9 January 2020 / Accepted: 16 January 2020 / Published: 23 January 2020
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications)
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.
Keywords: weibull distribution; stochastic diffusion process; likelihood estimation; statistical computation; simulation; age dependency ratio weibull distribution; stochastic diffusion process; likelihood estimation; statistical computation; simulation; age dependency ratio
MDPI and ACS Style

Nafidi, A.; Bahij, M.; Gutiérrez-Sánchez, R.; Achchab, B. Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example. Mathematics 2020, 8, 160.

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