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

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.

Stochastic Growth Models for the Spreading of Fake News

“…where the last equality follows from (8). By Equation (1), we have that F(t) is a continuous function.…”

“…It has been pointed out in various recent investigations on population dynamics that problems concerning differential equations of the form (2) can, in some instances, be expressed in a different way (cf. [3,[6][7][8]). In this vein, the present section is devoted to the determination of a different formulation of Equation ( 2), introducing a time-dependent growth rate.…”

“…Over the years, several sigmoidal curves have been introduced, such as Gompertz (see Tan [1]), Korf (introduced for the first time in Korf [2]), logistic (see, for instance, Di Crescenzo and Paraggio [3]), Bertalanffy-Richards (Richards [4]), and other generalizations of already existing models (as in Asadi et al [5], Di Crescenzo and Spina [6], Di Crescenzo et al [7,8]). The fields of possible applications of sigmoidal models are various and range from software reliability (see Erto et al [9]) to biology (as in Brauer and Castillo-Chavez [10]) and economics (see, for example, Smirnov and Wang [11]).…”