Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean.

Antonio Di Crescenzo, Paola Paraggio, Patricia Román-Román, Francisco Torres-Ruiz

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Article in Statistical papers (Berlin, Germany), 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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4 authors.

Antonio Di CrescenzoDipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano, SA Italy.ORCID 0000-0003-4751-7341

Paola ParaggioDipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano, SA Italy.ORCID 0000-0002-3308-7937

Patricia Román-RománDepartment of Statistics and Operations Research, Faculty of Sciences, University of Granada, 18071 Granada, Spain.ORCID 0000-0001-7752-8290

Francisco Torres-RuizDepartment of Statistics and Operations Research, Faculty of Sciences, University of Granada, 18071 Granada, Spain.ORCID 0000-0001-6254-2209

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

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.

Indexed as

Asymptotic distributionFirst-passage-timeFirst-passage-time location functionLognormal diffusion processMaximum likelihood estimationMulti-sigmoidal growth

Identifiers

PMID36062139

DOI10.1007/s00362-022-01349-1

PMCPMC9419654

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