Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds.
AU - Eastoe, Emma F.
AU - Tawn, Jon
PY - 2012/3
Y1 - 2012/3
N2 - A standard approach to model the extreme values of a stationaryprocess is the peaks over threshold method, which consists of imposinga high threshold, identifying clusters of exceedances of thisthreshold, and fitting the maximum value from each cluster using thegeneralised Pareto distribution. This approach is strongly justifiedby underlying asymptotic theory. We propose an alternative model forthe distribution of the cluster maxima which accounts for thesub-asymptotic theory of extremes of a stationary process. This newdistribution is a product of two terms, one for the marginaldistribution of exceedances and the other for the dependence structureof the exceedance values within a cluster. We illustrate theimprovement in fit, measured by the root mean square error of theestimated quantiles, offered by the new distribution over the peaksover thresholds analysis using simulated and hydrological data, and wesuggest a diagnostic tool to help identify when the proposed model islikely to lead to such an improvement in fit.
AB - A standard approach to model the extreme values of a stationaryprocess is the peaks over threshold method, which consists of imposinga high threshold, identifying clusters of exceedances of thisthreshold, and fitting the maximum value from each cluster using thegeneralised Pareto distribution. This approach is strongly justifiedby underlying asymptotic theory. We propose an alternative model forthe distribution of the cluster maxima which accounts for thesub-asymptotic theory of extremes of a stationary process. This newdistribution is a product of two terms, one for the marginaldistribution of exceedances and the other for the dependence structureof the exceedance values within a cluster. We illustrate theimprovement in fit, measured by the root mean square error of theestimated quantiles, offered by the new distribution over the peaksover thresholds analysis using simulated and hydrological data, and wesuggest a diagnostic tool to help identify when the proposed model islikely to lead to such an improvement in fit.
KW - cluster maxima, extremal index, generalised Pareto distribution, L-moments, peaks over thresholds
U2 - 10.1093/biomet/asr078
DO - 10.1093/biomet/asr078
M3 - Journal article
VL - 99
SP - 43
EP - 55
JO - Biometrika
JF - Biometrika
SN - 1464-3510
IS - 1
ER -