Skip to main content
SpringerLink
Log in

A note on characterizations of multivariate stable distributions

  • Distributions
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

Several characterizations of multivariate stable distributions together with a characterization of multivariate normal distributions and multivariate stable distributions with Cauchy marginals are given. These are related to some standard characterizations of marcinkiewicz.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Eaton, M. L. (1966). Characterization of distributions by the identical distributions of linear forms, J. Appl. Probab., 3, 481–494.

    Google Scholar 

  • Feldheim, M. E. (1937). Etude de la stabilité des lois de probabilitieś, These de la Faculté des Sciences de Paris.

  • Gupta, A. K., Nguyen, T. T. and Zeng, W. B. (1989a). Conditions for stability of laws with all projections stable, Tech. Report, 89–08, Department of Mathematics and Statistics, Bowling Green State University, Ohio.

    Google Scholar 

  • Gupta, A. K., Nguyen, T. T. and Zeng, W. G. (1989b). On a conditional Cauchy functional equation of several variables and a characterization of multivariate stable distributions. Tech. Report, 89–02, Department of Mathematics and Statistics, Bowling Green State University, Ohio.

    Google Scholar 

  • Kagan, A. M., Linnik, Y. V. and Rao, C. R. (1973). Characterization Problems in Mathematical Statistics, Wiley, New York.

    Google Scholar 

  • Kimeldorf, G. and Sampson, A. R. (1975). One-parameter families of bivariate distributions with fixed marginals, Comm. Statist., 4, 293–301.

    Google Scholar 

  • Lévy, P. (1924). Théorie des erreurs: La Loi de Gauss et les exceptionelles, Bull. Soc. Math. France, 52, 49–85.

    Google Scholar 

  • Lévy, P. (1937). Théorie de l'addition des variables Aléatoires, 2nd ed., Gauthier Villars, Paris.

    Google Scholar 

  • Marcus, D. J. (1983). Non-stable laws with all projections stable, Z. Wahrsch. Verw. Gebiete, 64, 139–156.

    Google Scholar 

  • Paulauskas, V. J. (1976). Some remarks on multivariate stable distributions, J. Multivariate Anal., 6, 356–368.

    Google Scholar 

  • Press, S. J. (1972). Multivariate stable distributions, J. Multivariate Anal., 2, 444–462.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematies and Statistics, Bowling Green State University, 43403, Bowling Green, OH, U.S.A.

    Truc T. Nguyen

  2. Department of Mathematics and Statistics, University of Pittsburgh, 15260, Pittsburgh, PA, U.S.A.

    Allan R. Sampson

Authors
  1. Truc T. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Allan R. Sampson
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported, in part, by the Air Force Office of Scientific Research under Contract AFOSR 84-0113. Reproduction in whole or part is permitted for any purpose of the United States Government.

About this article

Cite this article

Nguyen, T.T., Sampson, A.R. A note on characterizations of multivariate stable distributions. Ann Inst Stat Math 43, 793–801 (1991). https://doi.org/10.1007/BF00121655

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00121655

Key words and phrases

Search

Navigation