<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application

Laboratory of Analysis and Modeling Systems for Decision Support

Hassan First University of Settat, National School of Applied Sciences

Departamento de Estadística e Investigación Operativa, Faculty of sciences, Campus de Fuentenueva

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application

Published Online: Feb 01, 2023

Page range: 127 - 140

Received: Dec 21, 2022

Accepted: Jan 22, 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0009

Keywords
Stochastic diffusion model, Pareto distribution, Statistical inference, Simulated annealing method, Nonlinear regression, Child mortality rate

© 2023 Ahmed Nafidi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application

Published Online: Feb 01, 2023

Page range: 127 - 140

Received: Dec 21, 2022

Accepted: Jan 22, 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0009

KeywordsStochastic diffusion model, Pareto distribution, Statistical inference, Simulated annealing method, Nonlinear regression, Child mortality rate

© 2023 Ahmed Nafidi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Stochastic diffusion model, Pareto distribution, Statistical inference, Simulated annealing method, Nonlinear regression, Child mortality rate