Hyperbolastic type-III diffusion process: Obtaining from the generalized Weibull diffusion process Barrera, Antonio Román Román, Patricia Torres Ruiz, Francisco De Asís Growth curves Generalized Weibull curve Hyperbolastic models Inference in diffusion processes 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. 2019-12-05T11:17:07Z 2019-12-05T11:17:07Z 2019-11-04 info:eu-repo/semantics/article Barrera, A., Román-Roán, P., & Torres-Ruiz, F. (2019). Hyperbolastic type-III diffusion process: Obtaining from the generalized Weibull diffusion process. Mathematical biosciences and engineering: MBE, 17(1), 814-833. http://hdl.handle.net/10481/58209 10.3934/mbe.2020043 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España American Institute of Mathematical Sciences