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Bayesian analysis of extreme values by mixture modelling. (English) Zbl 1053.62061

It is supposed that the observed exceedances over some fixed threshold are generated by a Poisson process with intensity \[ \Lambda_y= ( 1+\xi(y-\mu)/ \psi)^{-1/\xi}, \] where \(\mu\) is the location, \(\psi\) is the scale and \(\xi\) is the shape parameter. A Bayesian analysis technique is described for the parameter \(\eta=(\mu,\psi,\xi)\) with a prior according to the mixture distribution \(\sum_{j=1}^k w_j p_j(\cdot\mid\delta_j)\) (here \(w_j\), \(\delta_j\) and \(k\) are hyperparameters). This construction allows the description of heterogeneous data. An application to insurance claim data is presented. Markov Chain Monte Carlo is used for the prior evaluation.

MSC:

62G32 Statistics of extreme values; tail inference
62F15 Bayesian inference
62M09 Non-Markovian processes: estimation
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