Asymptotic Expansions for Heavy-Tailed Data

Giancarlo Pastor, Inmaculada Mora-Jimenez, Antonio J. Caamano, Riku Jäntti

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

Abstract

Heavy-tailed distributions are present in the characterization of different modern systems such as high-resolution imaging, cloud computing, and cognitive radio networks. Commonly, the cumulants of these distributions cannot be defined from a certain order, and this restricts the applicability of traditional methods. To fill this gap, the present letter extends the traditional Edgeworth and Cornish-Fisher expansions, which are based on the cumulants, to analogous asymptotic expansions based on the log-cumulants. The proposed expansions inherit the capability of log-cumulants to characterize heavy-tailed distributions and parallel traditional expansions. Thus, they are readily implemented. Interestingly, the proposed expansions are applicable for light-tailed distributions as well.

Original languageEnglish
Article number7400987
Pages (from-to)444-448
Number of pages5
JournalIEEE Signal Processing Letters
Volume23
Issue number4
DOIs
Publication statusPublished - Apr 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Cornish-Fisher
  • Edgeworth
  • expansions
  • heavy-tailed distributions
  • Mellin transform
  • second kind statistics
  • ALPHA-STABLE DISTRIBUTIONS

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