A new Gompertz-type diffusion process with application to random growth

Stochastic models describing growth kinetics are very important for predicting many biological phenomena. In this paper, a new Gompertz-type diffusion process is introduced, by means of which bounded sigmoidal growth patterns can be modeled by time-continuous variables. The main innovation of the process is that the bound can depend on the initial value, a situation that is not provided by the models considered to date. building the model, a comprehensive study is presented, including its main characteristics and a simulation of sample paths. With the aim of applying this model to real-life situations, and given its possibilities in forecasting via the mean function, discrete sampling based inference is developed. The likelihood equations are not directly solvable, and because of difficulties that arise with the usual numerical methods employed to solve them, an iterative procedure is proposed. The possibilities of the new process are illustrated by means of an application to real data, concretely, to growth in rabbits.