Parameter Estimation for the Tail Distribution of a Random Sequence

Abstract

The tail Y_t = X_t – u of a random sequence {X_t ∈ , t ∈ } with identically distributed X_t is approximated by the generalized Pareto distribution according to the extreme value theory, wherein Y_t 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 Y_t, provided that there is independence between the clusters of Y_t. The estimation variances and confidence intervals can be estimated by the jackknife method. The approaches are theoretically discussed and verified by extensive numerical researches.

Keywords:

• Declustering
• Extreme value
• Generalized Pareto distribution
• Jackknife
• Peak over threshold
• Random sequence
• Tail

Mathematics Subject Classification:

• 62F40
• 60G70

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.