T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms

Antonio Barrera, Patricia Román-Román and Francisco Torres-Ruiz
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Antonio Barrera: Departamento de Análisis Matemático, Estadística e Investigación Operativa y Matemática Aplicada, Facultad de Ciencias, Universidad de Málaga, Bulevar Louis Pasteur, 31, 29010 Málaga, Spain
Patricia Román-Román: Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla 11, 18001 Granada, Spain
Francisco Torres-Ruiz: Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla 11, 18001 Granada, Spain

Mathematics, 2021, vol. 9, issue 9, 1-20

Abstract: The main objective of this work is to introduce a stochastic model associated with the one described by the T-growth curve, which is in turn a modification of the logistic curve. By conveniently reformulating the T curve, it may be obtained as a solution to a linear differential equation. This greatly simplifies the mathematical treatment of the model and allows a diffusion process to be defined, which is derived from the non-homogeneous lognormal diffusion process, whose mean function is a T curve. This allows the phenomenon under study to be viewed in a dynamic way. In these pages, the distribution of the process is obtained, as are its main characteristics. The maximum likelihood estimation procedure is carried out by optimization via metaheuristic algorithms. Thanks to an exhaustive study of the curve, a strategy is obtained to bound the parametric space, which is a requirement for the application of various swarm-based metaheuristic algorithms. A simulation study is presented to show the validity of the bounding procedure and an example based on real data is provided.

Keywords: growth curves; diffusion processes; inference on diffusion processes; metaheuristic algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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