IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i20p3781-d941491.html
   My bibliography  Save this article

A New Point Process Regression Extreme Model Using a Dirichlet Process Mixture of Weibull Distribution

Author

Listed:
  • Yingjie Wang

    (State Key Laboratory of Mechanics and Control of Mechanical Structures, School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

  • Xinsheng Liu

    (State Key Laboratory of Mechanics and Control of Mechanical Structures, School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

Abstract

The extreme value theory is widely used in economic and environmental domains, it aims to study the stochastic extreme behaviors associated with rare events. In this context, we consider a new mixture model for extremal events analysis, including a Dirichlet process mixture of Weibull (DPMW) distribution below the threshold and the point process (PP) extreme model for the upper tail. This model developed a regression structure for the PP extreme model parameters, which explains the variation of the exceedance through all tail parameters. The estimation of the model parameters is performed under the Bayesian paradigm, applying the Markov chains Monte Carlo (MCMC) method. The model is applied to both simulation and real environmental data to demonstrate the performance in extrapolating extreme events.

Suggested Citation

  • Yingjie Wang & Xinsheng Liu, 2022. "A New Point Process Regression Extreme Model Using a Dirichlet Process Mixture of Weibull Distribution," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3781-:d:941491
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/20/3781/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/20/3781/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. V. Chavez‐Demoulin & A. C. Davison, 2005. "Generalized additive modelling of sample extremes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 207-222, January.
    2. Stuart G. Coles & Jonathan A. Tawn, 1996. "A Bayesian Analysis of Extreme Rainfall Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 463-478, December.
    3. Paul J. Northrop & Nicolas Attalides & Philip Jonathan, 2017. "Cross-validatory extreme value threshold selection and uncertainty with application to ocean storm severity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 93-120, January.
    4. MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
    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. Juan Gonzalez & Daniela Rodriguez & Mariela Sued, 2013. "Threshold selection for extremes under a semiparametric model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 481-500, November.
    2. M. Carvalho & S. Pereira & P. Pereira & P. Zea Bermudez, 2022. "An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 222-239, June.
    3. Ross Towe & Jonathan Tawn & Emma Eastoe & Rob Lamb, 2020. "Modelling the Clustering of Extreme Events for Short-Term Risk Assessment," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 32-53, March.
    4. E. Zanini & E. Eastoe & M. J. Jones & D. Randell & P. Jonathan, 2020. "Flexible covariate representations for extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 31(5), August.
    5. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
    6. António Rua & Miguel de Carvalho, 2010. "Nonstationary Extremes and the US Business Cycle," Working Papers w201003, Banco de Portugal, Economics and Research Department.
    7. Yun Feng & Weijie Hou & Yuping Song, 2024. "Tail risk forecasting and its application to margin requirements in the commodity futures market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(5), pages 1513-1529, August.
    8. D. J. Rasmussen & Scott Kulp & Robert E. Kopp & Michael Oppenheimer & Benjamin H. Strauss, 2022. "Popular extreme sea level metrics can better communicate impacts," Climatic Change, Springer, vol. 170(3), pages 1-17, February.
    9. Christoph Marty & Juliette Blanchet, 2012. "Long-term changes in annual maximum snow depth and snowfall in Switzerland based on extreme value statistics," Climatic Change, Springer, vol. 111(3), pages 705-721, April.
    10. Philémon Gamet & Jonathan Jalbert, 2022. "A flexible extended generalized Pareto distribution for tail estimation," Environmetrics, John Wiley & Sons, Ltd., vol. 33(6), September.
    11. Daouia, Abdelaati & Gardes, Laurent & Girard, Stephane, 2011. "On kernel smoothing for extremal quantile regression," LIDAM Discussion Papers ISBA 2011031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Hongyu An & Boping Tian, 2024. "Varying Index Coefficient Model for Tail Index Regression," Mathematics, MDPI, vol. 12(13), pages 1-35, June.
    13. Cristiano Villa, 2017. "Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 95-118, March.
    14. Wang, Bing Xing & Ye, Zhi-Sheng, 2015. "Inference on the Weibull distribution based on record values," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 26-36.
    15. Francesca Biagini & Tobias Huber & Johannes G. Jaspersen & Andrea Mazzon, 2021. "Estimating extreme cancellation rates in life insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 971-1000, December.
    16. Gardes, Laurent & Girard, Stéphane & Lekina, Alexandre, 2010. "Functional nonparametric estimation of conditional extreme quantiles," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 419-433, February.
    17. Chiara Lattanzi & Manuele Leonelli, 2019. "A changepoint approach for the identification of financial extreme regimes," Papers 1902.09205, arXiv.org.
    18. Tong Siu Tung Wong & Wai Keung Li, 2015. "Extreme values identification in regression using a peaks-over-threshold approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 566-576, March.
    19. Schaumburg, Julia, 2012. "Predicting extreme value at risk: Nonparametric quantile regression with refinements from extreme value theory," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4081-4096.
    20. Murphy-Barltrop, C.J.R. & Wadsworth, J.L., 2024. "Modelling non-stationarity in asymptotically independent extremes," Computational Statistics & Data Analysis, Elsevier, vol. 199(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:gam:jmathe:v:10:y:2022:i:20:p:3781-:d:941491. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.