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 diffusion 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.
Highlights
Many researchers from a variety of fields have focused their efforts on modeling dynamic systems related to growth phenomena
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
Growth curves are commonly used in several fields of research to describe dynamical phenomena
Summary
Many researchers from a variety of fields have focused their efforts on modeling dynamic systems related to growth phenomena. Not all the previous diffusion processes verify that their mean function is a growth curve of the same type as the one associated with the starting deterministic model For this reason, some authors have focused their efforts on obtaining diffusion processes whose mean function is a specific growth curve, which is useful in real applications in which a certain growing pattern is observed. Some authors have focused their efforts on obtaining diffusion processes whose mean function is a specific growth curve, which is useful in real applications in which a certain growing pattern is observed Along this line we may mention the works [34, 35, 36], focused on the Bertalanffy, logistic and Richards curves respectively, and more recently [37, 38] whose goals are the hyperbolastic type-I and the multisigmoidal Gompertz curves, respectively.
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