IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v182y2021icp25-38.html
   My bibliography  Save this article

A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation

Author

Listed:
  • Nafidi, Ahmed
  • El Azri, Abdenbi

Abstract

Stochastic diffusion models have extensive areas of applications. They have been the object of particular attention in diverse fields of science such as biology, physics, chemistry, medical science and mathematical finance. In this paper, we present a new non-homogeneous stochastic diffusion process, in which the mean function is proportional to the growth curve of the Lundqvist–Korf. We first analyze the main features of the process including the transition probability density function and the mean functions. We then estimate the parameters of the model by the maximum likelihood method using discrete sampling after which we propose the simulated annealing algorithm to solve the likelihood equations. Finally, in order to highlight the utility of this methodology, we include the results obtained from several examples of simulation.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:25-38
    DOI: 10.1016/j.matcom.2020.10.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420303700
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2020.10.022?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. 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.
    2. 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.
    3. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2009. "The trend of the total stock of the private car-petrol in Spain: Stochastic modelling using a new gamma diffusion process," Applied Energy, Elsevier, vol. 86(1), pages 18-24, January.
    4. 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.
    5. 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.
    6. Gutiérrez, R. & Nafidi, A. & Gutiérrez Sánchez, R., 2005. "Forecasting total natural-gas consumption in Spain by using the stochastic Gompertz innovation diffusion model," Applied Energy, Elsevier, vol. 80(2), pages 115-124, February.
    7. Vera, J. Fernando & Di­az-Garci­a, Jose A., 2008. "A global simulated annealing heuristic for the three-parameter lognormal maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5055-5065, August.
    8. A. Katsamaki & C. H. Skiadas, 1995. "Analytic solution and estimation of parameters on a stochastic exponential model for a technological diffusion process," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(1), pages 59-75, March.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmed Nafidi & Abdenbi El Azri & Ramón Gutiérrez-Sánchez, 2023. "A Stochastic Schumacher Diffusion Process: Probability Characteristics Computation and Statistical Analysis," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-15, June.

    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. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2009. "The trend of the total stock of the private car-petrol in Spain: Stochastic modelling using a new gamma diffusion process," Applied Energy, Elsevier, vol. 86(1), pages 18-24, January.
    2. 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.
    3. 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.
    4. Gutiérrez-Sánchez, R. & Nafidi, A. & Pascual, A. & Ramos-Ábalos, E., 2011. "Three parameter gamma-type growth curve, using a stochastic gamma diffusion model: Computational statistical aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 234-243.
    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. Ahmed Nafidi & Meriem Bahij & Ramón Gutiérrez-Sánchez & Boujemâa Achchab, 2020. "Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example," Mathematics, MDPI, vol. 8(2), pages 1-11, January.
    7. 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.
    8. 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.
    9. 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.
    10. Badurally Adam, N.R. & Elahee, M.K. & Dauhoo, M.Z., 2011. "Forecasting of peak electricity demand in Mauritius using the non-homogeneous Gompertz diffusion process," Energy, Elsevier, vol. 36(12), pages 6763-6769.
    11. 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.
    12. Ahmed Nafidi & Abdenbi El Azri & Ramón Gutiérrez-Sánchez, 2023. "A Stochastic Schumacher Diffusion Process: Probability Characteristics Computation and Statistical Analysis," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-15, June.
    13. Gutiérrez, R. & Gutiérrez-Sánchez, R. & Nafidi, A., 2008. "Trend analysis and computational statistical estimation in a stochastic Rayleigh model: Simulation and application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 209-217.
    14. Gao, Mingyun & Yang, Honglin & Xiao, Qinzi & Goh, Mark, 2022. "A novel method for carbon emission forecasting based on Gompertz's law and fractional grey model: Evidence from American industrial sector," Renewable Energy, Elsevier, vol. 181(C), pages 803-819.
    15. Serli Kiremitciyan & Ahmet Goncu & Tolga Umut Kuzubas, 2014. "A Comparison of Stochastic Models of Natural Gas Consumption," Working Papers 2014/10, Bogazici University, Department of Economics.
    16. Leung, Philip C.M. & Lee, Eric W.M., 2013. "Estimation of electrical power consumption in subway station design by intelligent approach," Applied Energy, Elsevier, vol. 101(C), pages 634-643.
    17. Gutiérrez, R. & Nafidi, A. & Gutiérrez Sánchez, R., 2005. "Forecasting total natural-gas consumption in Spain by using the stochastic Gompertz innovation diffusion model," Applied Energy, Elsevier, vol. 80(2), pages 115-124, February.
    18. Le Boulzec, Hugo & Delannoy, Louis & Andrieu, Baptiste & Verzier, François & Vidal, Olivier & Mathy, Sandrine, 2022. "Dynamic modeling of global fossil fuel infrastructure and materials needs: Overcoming a lack of available data," Applied Energy, Elsevier, vol. 326(C).
    19. Askari, S. & Montazerin, N. & Zarandi, M.H. Fazel, 2015. "Forecasting semi-dynamic response of natural gas networks to nodal gas consumptions using genetic fuzzy systems," Energy, Elsevier, vol. 83(C), pages 252-266.
    20. Zhu, L. & Li, M.S. & Wu, Q.H. & Jiang, L., 2015. "Short-term natural gas demand prediction based on support vector regression with false neighbours filtered," Energy, Elsevier, vol. 80(C), pages 428-436.

    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:eee:matcom:v:182:y:2021:i:c:p:25-38. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.