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Open AccessFeature PaperArticle

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

1
Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
2
Instituto de Matemáticas de la Universidad de Granada (IEMath-GR), Calle Ventanilla 11, 18001 Granada, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(6), 541; https://doi.org/10.3390/math7060541
Received: 15 May 2019 / Revised: 10 June 2019 / Accepted: 11 June 2019 / Published: 13 June 2019
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. View Full-Text
Keywords: multi-sigmoidal growth curves; diffusion processes; maximum likelihood estimation; model selection multi-sigmoidal growth curves; diffusion processes; maximum likelihood estimation; model selection
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Román-Román, P.; Serrano-Pérez, J.J.; Torres-Ruiz, F. A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise. Mathematics 2019, 7, 541.

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