IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v77y2008i2p209-217.html
   My bibliography  Save this article

Trend analysis and computational statistical estimation in a stochastic Rayleigh model: Simulation and application

Author

Listed:
  • Gutiérrez, R.
  • Gutiérrez-Sánchez, R.
  • Nafidi, A.

Abstract

This paper considers a stochastic model based on the homogeneous stochastic Rayleigh diffusion process. We first examine the main probabilistic characteristics of the model and describe, among other results, an explicit expression of the trends (both conditioned and nonconditioned) and, when it exists, the stationary distribution. We then obtain results of the statistical estimation of the corresponding parameters and consider the computational problems that may arise. In addition, we present an algorithm for the stochastic simulation of the sample path of the model based on the corresponding Ito stochastic differential equation. Finally, the model is applied to study the evolution of the production of thermal electricity in countries in the Maghreb region; the results obtained are in good statistical accord with the real data observed for the period 1980–2002.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:77:y:2008:i:2:p:209-217
    DOI: 10.1016/j.matcom.2007.08.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475407002376
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2007.08.017?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. L. Ferrante & S. Bompadre & L. Possati & L. Leone, 2000. "Parameter Estimation in a Gompertzian Stochastic Model for Tumor Growth," Biometrics, The International Biometric Society, vol. 56(4), pages 1076-1081, December.
    2. 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.
    3. Guerra, Maria Letizia & Stefanini, Luciano, 2000. "A comparative simulation study for estimating diffusion coefficient," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(3), pages 193-203.
    4. 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.
    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. 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.
    2. 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.
    3. Nenghui Kuang & Huantian Xie, 2013. "Large and moderate deviations in testing Rayleigh diffusion model," Statistical Papers, Springer, vol. 54(3), pages 591-603, August.

    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. 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. 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.
    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. 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.
    6. Giorno, Virginia & Román-Román, Patricia & Spina, Serena & Torres-Ruiz, Francisco, 2017. "Estimating a non-homogeneous Gompertz process with jumps as model of tumor dynamics," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 18-31.
    7. 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.
    8. 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.
    9. Szoplik, Jolanta, 2015. "Forecasting of natural gas consumption with artificial neural networks," Energy, Elsevier, vol. 85(C), pages 208-220.
    10. Peñasco, Cristina & del Río, Pablo & Romero-Jordán, Desiderio, 2017. "Gas and electricity demand in Spanish manufacturing industries: An analysis using homogeneous and heterogeneous estimators," Utilities Policy, Elsevier, vol. 45(C), pages 45-60.
    11. Ravnik, J. & Hriberšek, M., 2019. "A method for natural gas forecasting and preliminary allocation based on unique standard natural gas consumption profiles," Energy, Elsevier, vol. 180(C), pages 149-162.
    12. Potočnik, Primož & Soldo, Božidar & Šimunović, Goran & Šarić, Tomislav & Jeromen, Andrej & Govekar, Edvard, 2014. "Comparison of static and adaptive models for short-term residential natural gas forecasting in Croatia," Applied Energy, Elsevier, vol. 129(C), pages 94-103.
    13. Ahmet Goncu & Mehmet Oguz Karahan & Tolga Umut Kuzubas, 2019. "Forecasting Daily Residential Natural Gas Consumption: A Dynamic Temperature Modelling Approach," Bogazici Journal, Review of Social, Economic and Administrative Studies, Bogazici University, Department of Economics, vol. 33(1), pages 1-22.
    14. Mustafa Akpinar & Nejat Yumusak, 2016. "Year Ahead Demand Forecast of City Natural Gas Using Seasonal Time Series Methods," Energies, MDPI, vol. 9(9), pages 1-17, September.
    15. Giulio Mangano & Giovanni Zenezini & Anna Corinna Cagliano & Alberto De Marco, 2019. "The dynamics of diffusion of an electronic platform supporting City Logistics services," Operations Management Research, Springer, vol. 12(3), pages 182-198, December.
    16. Cabrales, Luis Enrique Bergues & Montijano, Juan I. & Schonbek, Maria & Castañeda, Antonio Rafael Selva, 2018. "A viscous modified Gompertz model for the analysis of the kinetics of tumors under electrochemical therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 96-110.
    17. Ahmad, Tanveer & Huanxin, Chen & Zhang, Dongdong & Zhang, Hongcai, 2020. "Smart energy forecasting strategy with four machine learning models for climate-sensitive and non-climate sensitive conditions," Energy, Elsevier, vol. 198(C).
    18. 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.
    19. 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.
    20. Li, Fengyun & Zheng, Haofeng & Li, Xingmei & Yang, Fei, 2021. "Day-ahead city natural gas load forecasting based on decomposition-fusion technique and diversified ensemble learning model," Applied Energy, Elsevier, vol. 303(C).

    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:77:y:2008:i:2:p:209-217. 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.