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Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors

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  • Patricia Román-Román

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

Abstract

Different versions of the lognormal diffusion process with exogenous factors have been used in recent years to model and study the behavior of phenomena following a given growth curve. In each case considered, the estimation of the model has been addressed, generally by maximum likelihood (ML), as has been the study of several characteristics associated with the type of curve considered. For this process, a unified version of the ML estimation problem is presented, including how to obtain estimation errors and asymptotic confidence intervals for parametric functions when no explicit expression is available for the estimators of the parameters of the model. The Gompertz-type diffusion process is used here to illustrate the application of the methodology.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:5:p:85-:d:148105
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    References listed on IDEAS

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    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.
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    7. Ramón Gutiérrez & Patrica Román & Francisco Torres, 2001. "Inference on some parametric functions in the univeriate lognormal diffusion process with exogenous factors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 357-373, December.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. 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. Patricia Román-Román & Sergio Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2021. "Using First-Passage Times to Analyze Tumor Growth Delay," Mathematics, MDPI, vol. 9(6), pages 1-14, March.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Pramesti Getut, 2023. "Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process," Monte Carlo Methods and Applications, De Gruyter, vol. 29(1), pages 1-32, March.
    7. 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.
    8. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "Hyperbolastic Models from a Stochastic Differential Equation Point of View," Mathematics, MDPI, vol. 9(16), pages 1-18, August.

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