Statistical analysis and first-passage-time applications of a lognormal diffusion process withmulti-sigmoidal logistic mean
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914658555789312 |
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| author | Di Crescenzo, Antonio Paraggio, Paola Román-Román, Patricia Torres-Ruiz, Francisco |
| author_facet | Di Crescenzo, Antonio Paraggio, Paola Román-Román, Patricia Torres-Ruiz, Francisco |
| contents | We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical inference, two procedures to find the maximum likelihood estimates of the unknown parameters are described. One is based on the resolution of the system of the critical points of the likelihood function, and the other is on the maximization of the likelihood function with the simulated annealing algorithm. A simulation study to validate the described strategies for finding the estimates is also presented, with a real application to epidemiological data. Special attention is also devoted to the first-passage-time problem of the considered diffusion process through a fixed boundary. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_15730 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Statistical analysis and first-passage-time applications of a lognormal diffusion process withmulti-sigmoidal logistic mean Di Crescenzo, Antonio Paraggio, Paola Román-Román, Patricia Torres-Ruiz, Francisco Methodology Probability Statistics Theory 92D25, 60J85, 60J70 We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical inference, two procedures to find the maximum likelihood estimates of the unknown parameters are described. One is based on the resolution of the system of the critical points of the likelihood function, and the other is on the maximization of the likelihood function with the simulated annealing algorithm. A simulation study to validate the described strategies for finding the estimates is also presented, with a real application to epidemiological data. Special attention is also devoted to the first-passage-time problem of the considered diffusion process through a fixed boundary. |
| title | Statistical analysis and first-passage-time applications of a lognormal diffusion process withmulti-sigmoidal logistic mean |
| topic | Methodology Probability Statistics Theory 92D25, 60J85, 60J70 |
| url | https://arxiv.org/abs/2401.15730 |