Distribution tails of sample quantiles and subexponentiality

Michael Braverman, Gennady Samorodnitsky

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)45-60
Number of pages16
JournalStochastic Processes and their Applications
Volume76
Issue number1
DOIs
StatePublished - 1 Aug 1998

Keywords

  • 60G70
  • Infinitely divisible processes
  • Lévy measure
  • Primary 60G17
  • Sample quantiles
  • Secondary 60E07
  • Subexponential distribution
  • Tail behavior

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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