IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v64y2023i5d10.1007_s00362-022-01349-1.html
   My bibliography  Save this article

Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean

Author

Listed:
  • Antonio Di Crescenzo

    (Università degli Studi di Salerno)

  • Paola Paraggio

    (Università degli Studi di Salerno)

  • Patricia Román-Román

    (University of Granada
    Institute of Mathematics of the University of Granada (IMAG))

  • Francisco Torres-Ruiz

    (University of Granada
    Institute of Mathematics of the University of Granada (IMAG))

Abstract

We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical inference, two procedures to find the maximum likelihood estimates of the unknown parameters are described. One is based on the resolution of the system of the critical points of the likelihood function, and the other is on the maximization of the likelihood function with the simulated annealing algorithm. A simulation study to validate the described strategies for finding the estimates is also presented, with a real application to epidemiological data. Special attention is also devoted to the first-passage-time problem of the considered diffusion process through a fixed boundary.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:5:d:10.1007_s00362-022-01349-1
    DOI: 10.1007/s00362-022-01349-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-022-01349-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-022-01349-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    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. Román, P. & Serrano, J.J. & Torres, F., 2008. "First-passage-time location function: Application to determine first-passage-time densities in diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4132-4146, April.
    6. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez, 2019. "Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    7. Antonio Di Crescenzo & Paola Paraggio, 2019. "Logistic Growth Described by Birth-Death and Diffusion Processes," Mathematics, MDPI, vol. 7(6), pages 1-28, May.
    8. Virginia Giorno & Amelia G. Nobile, 2019. "Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions," Mathematics, MDPI, vol. 7(6), pages 1-19, June.
    9. Oscar García, 2019. "Estimating reducible stochastic differential equations by conversion to a least-squares problem," Computational Statistics, Springer, vol. 34(1), pages 23-46, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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. Giorno, Virginia & Nobile, Amelia G., 2023. "On a time-inhomogeneous diffusion process with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    8. 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.
    9. 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.
    10. 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.
    11. Moriguchi, Kai, 2018. "An approach for deriving growth equations for quantities exhibiting cumulative growth based on stochastic interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1150-1163.
    12. 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.
    13. Giorno, Virginia & Nobile, Amelia G., 2022. "On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    14. Antonio Di Crescenzo & Paola Paraggio & Serena Spina, 2023. "Stochastic Growth Models for the Spreading of Fake News," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    15. Nafidi, A. & Bahij, M. & Achchab, B. & Gutiérrez-Sanchez, R., 2019. "The stochastic Weibull diffusion process: Computational aspects and simulation," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 575-587.
    16. Nafidi, Ahmed & El Azri, Abdenbi, 2021. "A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 25-38.
    17. 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.
    18. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez, 2019. "Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    19. Virginia Giorno & Amelia G. Nobile, 2019. "Restricted Gompertz-Type Diffusion Processes with Periodic Regulation Functions," Mathematics, MDPI, vol. 7(6), pages 1-19, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:64:y:2023:i:5:d:10.1007_s00362-022-01349-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.