Stochastic Pareto diffusion process: Statistical analysis and computational issues. Simulation and Application
Metadatos
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Materia
Stochastic diffusion model Pareto distribution Statistical inference Simulated annealing method Nonlinear regression Child mortality rate
Fecha
2023-02-01Referencia bibliográfica
Nafidi,A.,Makroz,I.,Achchab,B. & Gutiérrez-Sánchez,R.(2023).Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application. Moroccan Journal of Pure and Applied Analysis,9(1) 127-140. [https://doi.org/10.2478/mjpaa-2023-0009]
Patrocinador
A-FQM-228-UGR18. Proyectos I+D+i del Programa Operativo FEDER 2018 Junta de AndaluciaResumen
We propose a novel diffusion process having a mean function equal to the Pareto probability
density function up to a constant of proportionality. We examine the probabilistic properties of the proposed
model. Then, referring to the problem of statistical inference, we describe the approach employed to
tackle the issue of obtaining parameter estimates by maximizing the likelihood function based on discrete
sampling. This estimation reduces to solving a set of complex equations, that is accomplished using the
simulated annealing algorithm. A simulation study is also given to validate the methodology presented.
Finally, using a real-world example of the Moroccan child mortality rate, we obtain the fits and forecasts by
employing the suggested stochastic process and nonlinear regression model.