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Characterization of a Marshall-Olkin type class of distributions

  • Pietro Muliere
  • Marco Scarsini
Article

Summary

A class of bivariate distributions that generalize Marshall-Olkin's one is characterized through a functional equation which involves two associative operations. The obtained distributions concentrate positive mass on the linex=y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function.

Key words and phrases

Characterization functional equation Marshall-Olkin distribution lack of memory property copula 

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References

  1. [1]
    Aczél, J. (1966).Lectures on Functional Equations and their Applications, Academic Press, New York.MATHGoogle Scholar
  2. [2]
    Basu, A. P. and Block, H. W. (1975). On characterizing univariate and multivariate exponential distributions with applications,Statistical Distributions in Scientific Work, (eds. G. P. Patil, S. Kotz and J. Ord),3, D. Reidel, Dordrecht-Boston, 399–421.Google Scholar
  3. [3]
    Castagnoli, E. (1978). Sulle operazioni associative tra variabili casuali,Rivista di Matematica per le Scienze Economiche e Sociali,1, 67–80.MATHMathSciNetGoogle Scholar
  4. [4]
    Castagnoli, E. and Muliere, P. (1984). Su una equazione funzionale e alcuni problemi di caratterizzazione,Tech. Report No. 21, Istituto di Matematica Finanziaria, Università di Parma.Google Scholar
  5. [5]
    Galambos, J. and Kotz, S. (1978).Characterizations of Probability Distributions, Springer-Verlag, Berlin-New York.MATHGoogle Scholar
  6. [6]
    Genest, C. and MacKay, R. J. (1986). Copules archimédiennes et familles de lois bidimensionelles dont les marges sont données,Canad. J. Statist.,14, 145–159.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Kimeldorf, G. and Sampson, A. R. (1978). Monotone dependence,Ann. Statist,6, 895–903.MATHMathSciNetGoogle Scholar
  8. [8]
    Marshall, A. W. and Olkin, I. (1967). A multivariate exponential distribution,J. Amer. Statist. Ass.,62, 30–49.MATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Moeschberger, M. L. (1974). Life tests under dependent competing causes of failure,Technometrics,16, 39–47.MATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    Muliere, P. (1984). Una nota su operazioni associative, trasformate integrali e problemi di caratterizzazione in statistica,Rivista di Matematica per le Scienze Economiche e Sociali,7, 79–93.MATHMathSciNetCrossRefGoogle Scholar
  11. [11]
    Scarsini, M. (1984). On measures of concordance,Stochastica,8, 201–218.MATHMathSciNetGoogle Scholar
  12. [12]
    Schweizer, B. and Sklar, A. (1983).Probabilistic Metric Spaces, North Holland, New York-Amsterdam.MATHGoogle Scholar
  13. [13]
    Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges,Publications de l'Institut de Statistique de l'Universitè de Paris,8, 229–231.MathSciNetGoogle Scholar
  14. [14]
    Wang, Y. H. (1976). A functional equation and its application to the characterization of the Weibull and stable distributions,J. Appl. Probab, 13, 385–391.MATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1987

Authors and Affiliations

  • Pietro Muliere
    • 1
    • 2
  • Marco Scarsini
    • 1
    • 2
  1. 1.Universitá Degli Studi di PaviaPaviaItalia
  2. 2.Universitá Degli Studi di ParmaParmaItalia

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