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Parameter Estimation for the Tail Distribution of a Random Sequence
Authors:Mathias Raschke
Institution:Fa. M. Raschke (company) , Leipzig , Germany
Abstract:The tail Yt = Xt – u of a random sequence {Xt ∈ /></span>, t ∈ <span class= /></span>} with identically distributed X<sub>t</sub> is approximated by the generalized Pareto distribution according to the extreme value theory, wherein Y<sub>t</sub> 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<sub>t</sub>, provided that there is independence between the clusters of Y<sub>t</sub>. The estimation variances and confidence intervals can be estimated by the jackknife method. The approaches are theoretically discussed and verified by extensive numerical researches.</td> </tr> <tr> <td align=
Keywords:Declustering  Extreme value  Generalized Pareto distribution  Jackknife  Peak over threshold  Random sequence  Tail
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