A hyperbolastic type-I diffusion process: Parameter estimation by means of the firefly algorithm

Antonio Barrera; Patricia Román-Román; Francisco Torres-Ruiz

doi:10.1016/j.biosystems.2017.11.001

A hyperbolastic type-I diffusion process: Parameter estimation by means of the firefly algorithm

Biosystems. 2018 Jan:163:11-22. doi: 10.1016/j.biosystems.2017.11.001. Epub 2017 Nov 9.

Authors

Antonio Barrera¹, Patricia Román-Román², Francisco Torres-Ruiz³

Affiliations

¹ Departamento de Matemática Aplicada, E.T.S.I. Informática, Bulevar Louis Pasteur, 35, Campus de Teatinos, Universidad de Málaga, 29071 Málaga, Spain. Electronic address: antonio.barrera@uma.es.
² Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, s/n, Campus de Fuentenueva, Universidad de Granada, 18071 Granada, Spain. Electronic address: proman@ugr.es.
³ Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, s/n, Campus de Fuentenueva, Universidad de Granada, 18071 Granada, Spain. Electronic address: fdeasis@ugr.es.

PMID: 29129822
DOI: 10.1016/j.biosystems.2017.11.001

Abstract

A stochastic diffusion process, whose mean function is a hyperbolastic curve of type I, is presented. The main characteristics of the process are studied and the problem of maximum likelihood estimation for the parameters of the process is considered. To this end, the firefly metaheuristic optimization algorithm is applied after bounding the parametric space by a stagewise procedure. Some examples based on simulated sample paths and real data illustrate this development.

Keywords: Diffusion process; Firefly algorithm; Hyperbolastic curve.

MeSH terms

Algorithms*
Animals
Diffusion
Fireflies
Likelihood Functions
Stochastic Processes*