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Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds.

Eastoe, Emma F. and Tawn, Jon (2012) Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds. Biometrika, 99 (1). pp. 43-55. ISSN 1464-3510

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Abstract

A standard approach to model the extreme values of a stationary process is the peaks over threshold method, which consists of imposing a high threshold, identifying clusters of exceedances of this threshold, and fitting the maximum value from each cluster using the generalised Pareto distribution. This approach is strongly justified by underlying asymptotic theory. We propose an alternative model for the distribution of the cluster maxima which accounts for the sub-asymptotic theory of extremes of a stationary process. This new distribution is a product of two terms, one for the marginal distribution of exceedances and the other for the dependence structure of the exceedance values within a cluster. We illustrate the improvement in fit, measured by the root mean square error of the estimated quantiles, offered by the new distribution over the peaks over thresholds analysis using simulated and hydrological data, and we suggest a diagnostic tool to help identify when the proposed model is likely to lead to such an improvement in fit.

Item Type: Article
Journal or Publication Title: Biometrika
Uncontrolled Keywords: cluster maxima, extremal index, generalised Pareto distribution, L-moments, peaks over thresholds
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 26853
Deposited By: Dr Emma Eastoe
Deposited On: 31 Jul 2009 10:16
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 15:41
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/26853

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