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

Author

Listed:
  • Patricia Román-Román

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    Instituto de Matemáticas de la Universidad de Granada (IEMath-GR), Calle Ventanilla 11, 18001 Granada, Spain
    These authors contributed equally to this work.)

  • Juan José Serrano-Pérez

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Francisco Torres-Ruiz

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    Instituto de Matemáticas de la Universidad de Granada (IEMath-GR), Calle Ventanilla 11, 18001 Granada, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2019. "A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise," Mathematics, MDPI, vol. 7(6), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:541-:d:239640
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    References listed on IDEAS

    as
    1. Tang, Sanyi & Heron, Elizabeth A., 2008. "Bayesian inference for a stochastic logistic model with switching points," Ecological Modelling, Elsevier, vol. 219(1), pages 153-169.
    2. Gallagher, Brian, 2011. "Peak oil analyzed with a logistic function and idealized Hubbert curve," Energy Policy, Elsevier, vol. 39(2), pages 790-802, February.
    3. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2018. "Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors," Mathematics, MDPI, vol. 6(5), pages 1-13, May.
    4. Stan Lipovetsky, 2010. "Double logistic curve in regression modeling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1785-1793.
    5. Luz-Sant’Ana, Istoni & Román-Román, Patricia & Torres-Ruiz, Francisco, 2017. "Modeling oil production and its peak by means of a stochastic diffusion process based on the Hubbert curve," Energy, Elsevier, vol. 133(C), pages 455-470.
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    Cited by:

    1. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2020. "Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior," Mathematics, MDPI, vol. 8(2), pages 1-20, January.
    2. Petras Rupšys & Martynas Narmontas & Edmundas Petrauskas, 2020. "A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    3. Petras Rupšys, 2019. "Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures," Mathematics, MDPI, vol. 7(8), pages 1-22, August.
    4. Antonio Barrera & Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2021. "Two Multi-Sigmoidal Diffusion Models for the Study of the Evolution of the COVID-19 Pandemic," Mathematics, MDPI, vol. 9(19), pages 1-29, September.
    5. Eva María Ramos-Ábalos & Ramón Gutiérrez-Sánchez & Ahmed Nafidi, 2020. "Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    6. Antonio Di Crescenzo & Paola Paraggio & Patricia Román-Román & Francisco Torres-Ruiz, 2023. "Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean," Statistical Papers, Springer, vol. 64(5), pages 1391-1438, October.

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