On exceedances of high levels

S.Y. Novak and A. Xia

Stochastic Processes and their Applications, 2012, vol. 122, issue 2, 582-599

Abstract: The distribution of the excess process describing heights of extreme values can be approximated by the distribution of a Poisson cluster process. An estimate of the accuracy of such an approximation has been derived in [4] in terms of the Wasserstein distance. The paper presents a sharper estimate established in terms of the stronger total variation distance. We derive also a new bound to the accuracy of negative Binomial approximation to the distribution of the number of exceedances.

Keywords: Extreme values; Poisson cluster process; Compound Poisson approximation; Negative Binomial approximation; Total variation distance (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2011.09.003

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