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

Author

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  • 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
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    References listed on IDEAS

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    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.
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