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Quasi-conjugate Bayes estimates for GPD parameters and application to heavy tails modelling

Jean Diebolt 1 Mhamed-Ali El-Aroui 1 Myriam Garrido 1 Stéphane Girard 1
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558
Abstract : We present a quasi-conjugate Bayes approach for estimating Generalized Pareto Distribution (GPD) parameters, distribution tails and extreme quantiles within the Peaks-Over-Threshold framework. Damsleth conjugate Bayes structure on Gamma distributions is transfered to GPD. Bayes credibility intervals are defined, they provide assessment of the quality of the extreme events estimates. Posterior estimates are computed by Gibbs samplers with Hastings-Metropolis steps. Even if non-informative priors are used in this work, the suggested approach could incorporate informative priors, it brings solutions to the problem of estimating extreme events when data are scarce but expert opinion is available. It is shown that the obtained quasi-conjugate Bayes estimators compare well with the GPD standard estimators on simulated and real data sets.
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https://hal.inria.fr/inria-00071783
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 6:46:24 PM
Last modification on : Tuesday, October 13, 2020 - 4:24:04 PM
Long-term archiving on: : Sunday, April 4, 2010 - 8:45:09 PM

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Jean Diebolt, Mhamed-Ali El-Aroui, Myriam Garrido, Stéphane Girard. Quasi-conjugate Bayes estimates for GPD parameters and application to heavy tails modelling. [Research Report] RR-4803, INRIA. 2003. ⟨inria-00071783⟩

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