High Quantiles of Heavy-Tailed Distributions: Their Estimation

Authors:
N. M. Markovich
Affiliations:
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Venue:
Automation and Remote Control
Year:
2002

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Abstract

High quantiles of heavy-tailed distributions are estimated under the assumption that the tail is of Pareto type. The distribution of the logarithm of the estimate ratio to the true quantile is asymptotically normal. The same is also proved for the Weissman estimate.