Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example
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 analyz...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/2/160 |
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| author | Ahmed Nafidi Meriem Bahij Ramón Gutiérrez-Sánchez Boujemâa Achchab |
| author_facet | Ahmed Nafidi Meriem Bahij Ramón Gutiérrez-Sánchez Boujemâa Achchab |
| author_sort | Ahmed Nafidi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T20:21:54Z |
| format | Article |
| id | doaj.art-6c921b76a415424bbf9869807cc19d78 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-21T20:21:54Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6c921b76a415424bbf9869807cc19d782022-12-21T18:51:28ZengMDPI AGMathematics2227-73902020-01-018216010.3390/math8020160math8020160Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling ExampleAhmed Nafidi0Meriem Bahij1Ramón Gutiérrez-Sánchez2Boujemâa Achchab3Department of mathematics and informatics, LAMSAD, National School of Applied Sciences of Berrechid, University of Hassan 1, Avenue de l’université, BP 280, Berrechid 26100, MoroccoDepartment of mathematics and informatics, LAMSAD, National School of Applied Sciences of Berrechid, University of Hassan 1, Avenue de l’université, BP 280, Berrechid 26100, MoroccoDepartment of Statistics and Operational Research, University of Granada, Facultad de Ciencias, Campus de Fuentenueva, 18071 Granada, SpainDepartment of mathematics and informatics, LAMSAD, National School of Applied Sciences of Berrechid, University of Hassan 1, Avenue de l’université, BP 280, Berrechid 26100, MoroccoThis 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.https://www.mdpi.com/2227-7390/8/2/160weibull distributionstochastic diffusion processlikelihood estimationstatistical computationsimulationage dependency ratio |
| spellingShingle | Ahmed Nafidi Meriem Bahij Ramón Gutiérrez-Sánchez Boujemâa Achchab Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example Mathematics weibull distribution stochastic diffusion process likelihood estimation statistical computation simulation age dependency ratio |
| title | Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example |
| title_full | Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example |
| title_fullStr | Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example |
| title_full_unstemmed | Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example |
| title_short | Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example |
| title_sort | two parameter stochastic weibull diffusion model statistical inference and application to real modeling example |
| topic | weibull distribution stochastic diffusion process likelihood estimation statistical computation simulation age dependency ratio |
| url | https://www.mdpi.com/2227-7390/8/2/160 |
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