@misc{10481/93787,
year = {2024},
month = {8},
url = {https://hdl.handle.net/10481/93787},
abstract = {We analyze a modification of the Richards growth model by introducing a time-dependent
perturbation in the growth rate. This modification becomes effective at a special switching time,
which represents the first-crossing-time of the Richards growth curve through a given constant
boundary. The relevant features of the modified growth model are studied and compared
with those of the original one. A sensitivity analysis on the switching time is also performed.
Then, we define two different stochastic processes, i.e. a non-homogeneous linear birth–death
process and a lognormal diffusion process, such that their means identify to the growth
curve under investigation. For the diffusion process, we address the problem of parameters
estimation through the maximum likelihood method. The estimates are obtained via metaheuristic
algorithms (namely, Simulated Annealing and Ant Lion Optimizer). A simulation study
to validate the estimation procedure is also presented, together with a real application to
oil production in France. Special attention is devoted to the approximation of switching time
density, viewed as the first-passage-time density for the lognormal process.},
organization = {‘‘Ministerio de Ciencia e Innovación, Spain, under Grant PID2020-1187879GB-100, and ‘‘María de Maeztu’’},
organization = {Excellence Unit IMAG, reference CEX2020-001105-M, funded by MCIN/AEI/10.13039/501100011033/},
organization = {‘European Union
– Next Generation EU’ through MUR-PRIN 2022},
organization = {project 2022XZSAFN ‘‘Anomalous Phenomena on Regular and Irregular Domains:
Approximating Complexity for the Applied Sciences’’},
organization = {MUR-PRIN 2022 PNRR, project P2022XSF5H ‘‘Stochastic Models in
Biomathematics and Applications’’},
publisher = {Elsevier},
keywords = {Richards growth model},
keywords = {Non-homogeneous birth–death process},
keywords = {Lognormal diffusion process},
title = {A Bertalanffy–Richards growth model perturbed by a time-dependent pattern, statistical analysis and applications✩},
doi = {10.1016/j.cnsns.2024.108258},
author = {Di Crescenzo, Antonio and Paraggio, Paola and Torres-Ruiz, Francisco},
}