A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise

Patricia Román-Román, Juan José Serrano-Pérez and Francisco Torres-Ruiz
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Patricia Román-Román: Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
Juan José Serrano-Pérez: Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
Francisco Torres-Ruiz: Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain

Mathematics, 2019, vol. 7, issue 6, 1-18

Abstract: The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is introduced whose mean function is a curve of this type, concretely a transformation of the well-known Gompertz model after introducing in its expression a polynomial term. The maximum likelihood estimation of the parameters of the model is studied, and various criteria are provided for the selection of the degree of the polynomial when real situations are addressed. Finally, some simulated examples are presented.

Keywords: multi-sigmoidal growth curves; diffusion processes; maximum likelihood estimation; model selection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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