Extremes

, Volume 6, Issue 1, pp 25–47 | Cite as

Bayesian Analysis of Extreme Values by Mixture Modeling

  • Leonardo Bottolo
  • Guido Consonni
  • Petros Dellaportas
  • Antonio Lijoi

Abstract

Modeling of extreme values in the presence of heterogeneity is still a relatively unexplored area. We consider losses pertaining to several related categories. For each category, we view exceedances over a given threshold as generated by a Poisson process whose intensity is regulated by a specific location, shape and scale parameter. Using a Bayesian approach, we develop a hierarchical mixture prior, with an unknown number of components, for each of the above parameters. Computations are performed using Reversible Jump MCMC. Our model accounts for possible grouping effects and takes advantage of the similarity across categories, both for estimation and prediction purposes. Some guidance on the specification of the prior distribution is provided, together with an assessment of inferential robustness. The method is illustrated throughout using a data set on large claims against a well-known insurance company over a 15-year period.

heterogeneity insurance claim and loss partition predictive distribution reversible jump MCMC 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Leonardo Bottolo
    • 1
    • 2
  • Guido Consonni
    • 1
  • Petros Dellaportas
    • 2
  • Antonio Lijoi
    • 1
  1. 1.University of PaviaItaly
  2. 2.Athens University of EconomicsGreece

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