A tail estimator for the index of the stable paretian distribution

Stefan Mittnik, Marc S. Paolella, Svetlozar T. Rachev

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


A new tail estimator for the index α of stable Paretian distributions is considered. The problem of specifying integer k, which determines the tail area used for estimation, is investigated for all three estimators, and shown that the optimal k value for the new estimator is highly insensitive to the true value of index α. As a result, in contrast to existing tail estimators such as the widely used Hill estimator, a simple rule for choosing k can be established. Finally, the small sample properties of the new estimator are examined.

Original languageEnglish
Pages (from-to)1239-1262
Number of pages24
JournalCommunications in Statistics - Theory and Methods
Issue number5
StatePublished - 1998


  • Hill estimator
  • Pickands estimator
  • Stable distributions
  • Tail estimation


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