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A Stochastic Lomax Diffusion Process: Statistical Inference and Application

Author

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  • Ahmed Nafidi

    (Department of Mathematics and Informatics, National School of Applied Sciences, Hassan First University of Settat, LAMSAD, Avenue de l’université, Berrechid BP 280, Morocco
    These authors contributed equally to this work.)

  • Ilyasse Makroz

    (Department of Mathematics and Informatics, National School of Applied Sciences, Hassan First University of Settat, LAMSAD, Avenue de l’université, Berrechid BP 280, Morocco
    These authors contributed equally to this work.)

  • Ramón Gutiérrez Sánchez

    (Department of Statistics and Operational Research, Facultad de Ciencias, Campus de Fuentenueva, University of Granada, 18071 Granada, Spain
    These authors contributed equally to this work.)

Abstract

In this paper, we discuss a new stochastic diffusion process in which the trend function is proportional to the Lomax density function. This distribution arises naturally in the studies of the frequency of extremely rare events. We first consider the probabilistic characteristics of the proposed model, including its analytic expression as the unique solution to a stochastic differential equation, the transition probability density function together with the conditional and unconditional trend functions. Then, we present a method to address the problem of parameter estimation using maximum likelihood with discrete sampling. This estimation requires the solution of a non-linear equation, which is achieved via the simulated annealing method. Finally, we apply the proposed model to a real-world example concerning adolescent fertility rate in Morocco.

Suggested Citation

  • Ahmed Nafidi & Ilyasse Makroz & Ramón Gutiérrez Sánchez, 2021. "A Stochastic Lomax Diffusion Process: Statistical Inference and Application," Mathematics, MDPI, vol. 9(1), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:1:p:100-:d:474939
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    References listed on IDEAS

    as
    1. Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 438-465, September.
    2. Nafidi, A. & Gutiérrez, R. & Gutiérrez-Sánchez, R. & Ramos-Ábalos, E. & El Hachimi, S., 2016. "Modelling and predicting electricity consumption in Spain using the stochastic Gamma diffusion process with exogenous factors," Energy, Elsevier, vol. 113(C), pages 309-318.
    3. R. Gutiérrez & R. Gutiérrez‐Sánchez & A. Nafidi, 2009. "Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of Spain," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 385-405, May.
    4. Bo Martin Bibby & Michael SÛrensen, 1996. "A hyperbolic diffusion model for stock prices (*)," Finance and Stochastics, Springer, vol. 1(1), pages 25-41.
    5. R. Gutiérrez & J. M. Angulo & A. González & R. Pérez, 1991. "Inference in lognormal multidimensional diffusion processes with exogenous factors: Application to modelling in economics," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 7(4), pages 295-316, December.
    6. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2006. "Electricity consumption in Morocco: Stochastic Gompertz diffusion analysis with exogenous factors," Applied Energy, Elsevier, vol. 83(10), pages 1139-1151, October.
    Full references (including those not matched with items on IDEAS)

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