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

Author

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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
    Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla 11, 18001 Granada, Spain
    These authors contributed equally to this work.)

  • Patricia Román-Román

    (Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla 11, 18001 Granada, Spain
    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

    (Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla 11, 18001 Granada, Spain
    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.)

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.

Suggested Citation

  • Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms," Mathematics, MDPI, vol. 9(9), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:959-:d:543027
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    References listed on IDEAS

    as
    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. Mohammad A Tabatabai & Jean-Jacques Kengwoung-Keumo & Wayne M Eby & Sejong Bae & Juliette T Guemmegne & Upender Manne & Mona Fouad & Edward E Partridge & Karan P Singh, 2014. "Disparities in Cervical Cancer Mortality Rates as Determined by the Longitudinal Hyperbolastic Mixed-Effects Type II Model," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-18, September.
    3. Giacomo Ascione & Yuliya Mishura & Enrica Pirozzi, 2021. "Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 53-84, March.
    4. Román-Román, P. & Torres-Ruiz, F., 2015. "A stochastic model related to the Richards-type growth curve. Estimation by means of simulated annealing and variable neighborhood search," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 579-598.
    5. Rajasekar, S.P. & Pitchaimani, M., 2020. "Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    6. 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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