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A Bayesian Regularization Procedure for a Better Extremal Fit

Jean Diebolt 1 Myriam Garrido 1 Catherine Trottier 2
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558
Abstract : In Structural Reliability, special attention is devoted to model distribution tails. This is important when one wants to estimate the occurrence probability of rare events as critical failures, extreme charges, resistance measures, frequency of stressing events, etc. People try to find distribution models having a good overall fit to the data. Particularly, the distributions are strongly required to fit the upper observations and provide a good picture of the tail above the maximal observation. Specific goodness-of-fit tests such as the ET test can be constructed to check this tail fit. Then what can we do with distributions having a good central fit and a bad extremal fit ? We propose a regularization procedure, that is to say a procedure which preserves the general form of the initial distribution and allows a better fit in the distribution tail. It is based on Bayesian tools and takes the opinion of experts into account. Predictive distributions are proposed as model distributions. They are obtained as a mixture of the model family density functions according to the posterior distribution. Therefore, they are rather smooth and can easily be simulated. We numerically investigate this method on normal, lognormal, exponential, gamma and Weibull distributions. Our method is illustrated on both simulated and real data sets.
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https://hal.inria.fr/inria-00072411
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 9:53:17 AM
Last modification on : Tuesday, October 13, 2020 - 4:24:05 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:06:27 PM

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  • HAL Id : inria-00072411, version 1

Citation

Jean Diebolt, Myriam Garrido, Catherine Trottier. A Bayesian Regularization Procedure for a Better Extremal Fit. [Research Report] RR-4211, INRIA. 2001. ⟨inria-00072411⟩

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