@misc{10481/58209,
year = {2019},
month = {11},
url = {http://hdl.handle.net/10481/58209},
abstract = {The modeling of growth phenomena has become a matter of great interest in many different
fields of application and research. New stochastic models have been developed, and others have been
updated to this end. The present paper introduces a diffusion process whose main characteristic is that
its mean function belongs to a wide family of curves derived from the classic Weibull curve. The main
characteristics of the process are described and, as a particular case, a di usion process is considered
whose mean function is the hyperbolastic curve of type III, which has proven useful in the study of cell
growth phenomena. By studying its estimation we are able to describe the behavior of such growth
patterns. This work considers the problem of the maximum likelihood estimation of the parameters
of the process, including strategies to obtain initial solutions for the system of equations that must be
solved. Some examples are provided based on simulated sample paths and real data to illustrate the
development carried out.},
organization = {This work was supported in part by the Ministerio de Economía, Industria y Competitividad, Spain,
 under Grant MTM2017-85568-P.},
publisher = {American Institute of Mathematical Sciences},
keywords = {Growth curves},
keywords = {Generalized Weibull curve},
keywords = {Hyperbolastic models},
keywords = {Inference in diffusion processes},
title = {Hyperbolastic type-III diffusion process: Obtaining from the generalized Weibull diffusion process},
doi = {10.3934/mbe.2020043},
author = {Barrera, Antonio and Román Román, Patricia and Torres Ruiz, Francisco De Asís},
}