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 () and Francisco Torres-Ruiz ()
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Antonio Di Crescenzo: Università degli Studi di Salerno
Paola Paraggio: Università degli Studi di Salerno
Patricia Román-Román: University of Granada
Francisco Torres-Ruiz: University of Granada

Statistical Papers, 2023, vol. 64, issue 5, No 2, 1438 pages

Abstract: 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.

Keywords: Lognormal diffusion process; Multi-sigmoidal growth; Maximum likelihood estimation; Asymptotic distribution; First-passage-time; First-passage-time location function; 62M05; 60J70 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00362-022-01349-1

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