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

Yingjie Wang and Xinsheng Liu ()
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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

Mathematics, 2022, vol. 10, issue 20, 1-24

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.

Keywords: extreme value; mixture model; Dirichlet process mixture; regression structure; Bayesian inference (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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