Asymptotic properties of the partition function and applications in tail index inference of heavy-tailed data

Danijel Grahovac, Mofei Jia, Nikolai Leonenko*, Emanuele Taufer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution underlying the data both in independent identically distributed and weakly dependent cases. These results will be used to develop graphical and estimation methods for the tail index of a distribution. The performance of the tools proposed is analysed and compared with other methods by means of simulations and examples.

Original languageEnglish
Pages (from-to)1221-1242
Number of pages22
Issue number6
Publication statusPublished - 2 Nov 2015
Externally publishedYes


  • heavy tails
  • partition function
  • scaling function
  • tail index

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