Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application
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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2023-01-01
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| Series: | Moroccan Journal of Pure and Applied Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/mjpaa-2023-0009 |
| _version_ | 1811159345332748288 |
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| author | Nafidi Ahmed Makroz Ilyasse Achchab Boujemâa Gutiérrez-Sánchez Ramón |
| author_facet | Nafidi Ahmed Makroz Ilyasse Achchab Boujemâa Gutiérrez-Sánchez Ramón |
| author_sort | Nafidi Ahmed |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T05:39:30Z |
| format | Article |
| id | doaj.art-027b7acdff3948ffa3e86ddcc073c7fd |
| institution | Directory Open Access Journal |
| issn | 2351-8227 |
| language | English |
| last_indexed | 2024-04-10T05:39:30Z |
| publishDate | 2023-01-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Moroccan Journal of Pure and Applied Analysis |
| spelling | doaj.art-027b7acdff3948ffa3e86ddcc073c7fd2023-03-06T10:30:08ZengSciendoMoroccan Journal of Pure and Applied Analysis2351-82272023-01-019112714010.2478/mjpaa-2023-0009Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and ApplicationNafidi Ahmed0Makroz Ilyasse1Achchab Boujemâa2Gutiérrez-Sánchez Ramón3Laboratory of Analysis and Modeling Systems for Decision Support, Hassan First University of Settat, National School of Applied Sciences, 26100, Berrchid, MoroccoLaboratory of Analysis and Modeling Systems for Decision Support, Hassan First University of Settat, National School of Applied Sciences, 26100, Berrchid, MoroccoLaboratory of Analysis and Modeling Systems for Decision Support, Hassan First University of Settat, National School of Applied Sciences, 26100, Berrchid, MoroccoDepartamento de Estadística e Investigación Operativa, Faculty of sciences, Campus de Fuentenueva, Universidad de Granada, 18071, Granada, SpainWe 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.https://doi.org/10.2478/mjpaa-2023-0009stochastic diffusion modelpareto distributionstatistical inferencesimulated annealing methodnonlinear regressionchild mortality rate60h3565c3062m8662m2060h30 |
| spellingShingle | Nafidi Ahmed Makroz Ilyasse Achchab Boujemâa Gutiérrez-Sánchez Ramón Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application Moroccan Journal of Pure and Applied Analysis stochastic diffusion model pareto distribution statistical inference simulated annealing method nonlinear regression child mortality rate 60h35 65c30 62m86 62m20 60h30 |
| title | Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application |
| title_full | Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application |
| title_fullStr | Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application |
| title_full_unstemmed | Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application |
| title_short | Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application |
| title_sort | stochastic pareto diffusion process statistical analysis and computational issues simulation and application |
| topic | stochastic diffusion model pareto distribution statistical inference simulated annealing method nonlinear regression child mortality rate 60h35 65c30 62m86 62m20 60h30 |
| url | https://doi.org/10.2478/mjpaa-2023-0009 |
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