, Volume 78, Issue 5, pp 549–561 | Cite as

On estimating the tail index and the spectral measure of multivariate \(\alpha \)-stable distributions

  • Mohammad Mohammadi
  • Adel Mohammadpour
  • Hiroaki Ogata


We propose estimators for the tail index and the spectral measure of multivariate \(\alpha \)-stable distributions and derive their asymptotic properties. Simulation studies reveal the appropriateness of the estimators. Applications to financial data are also considered.


Asymptotic distribution Multivariate α-stable distribution Spectral measure Tail index estimation Generalized empirical likelihood estimation 

Mathematics Subject Classification

60E07 62H12 62G32 



The authors would like to thank an anonymous reviewer and Editor, Professor Norbert Henze, for their valuable comments and suggestions to improve the manuscript. They are also grateful to Professor John P. Nolan to provide access to STABLE package in R for improving the computations and Dr. Thaigo do Rego Sousa for his help in running the programs of GEVStableGarch package. The third author was supported by JSPS KAKENHI Grant Number 26870655.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Mohammad Mohammadi
    • 1
  • Adel Mohammadpour
    • 1
    • 3
  • Hiroaki Ogata
    • 2
  1. 1.Department of Statistics, Faculty of Mathematics and Computer ScienceAmirkabir University of Technology (Tehran Polytechnic)TehranIran
  2. 2.School of Business Administration, Faculty of Urban Liberal ArtsTokyo Metropolitan UniversityTokyoJapan
  3. 3.Department of EconomicsMcGill UniversityMontréalCanada

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