Distribution tails of sample quantiles and subexponentiality

Michael Braverman and Gennady Samorodnitsky

Stochastic Processes and their Applications, 1998, vol. 76, issue 1, 45-60

Abstract: We show that subexponentiality is not sufficient to guarantee that the distribution tail of a sample quantile of an infinitely divisible process is equivalent to the "tail" of the same sample quantile under the corresponding Lévy measure. However, such an equivalence result is shown to hold under either an assumption of an appropriately slow tail decay or an assumption on the structure of the process.

Keywords: Sample; quantiles; Tail; behavior; Infinitely; divisible; processes; Subexponential; distribution; Lévy; measure (search for similar items in EconPapers)
Date: 1998
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