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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.

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