Abstract
The tail Yt = Xt – u of a random sequence {Xt ∈ , t ∈
} with identically distributed Xt is approximated by the generalized Pareto distribution according to the extreme value theory, wherein Yt occurs in clusters because of the dependence in the random sequence. Nevertheless, the parameters of the generalized Pareto distribution are estimated by the same methods as in the case of independent and identically distributed Yt, provided that there is independence between the clusters of Yt. The estimation variances and confidence intervals can be estimated by the jackknife method. The approaches are theoretically discussed and verified by extensive numerical researches.
Acknowledgments
We would like to thank the editor and referees for their comments and suggestions. Furthermore, we are grateful to Valeska Klatt for help in proofreading.