An Analytical Characterization of the Exchangeable Wide-Sense Geometric Law

  • Jan-Frederik Mai
  • Matthias Scherer
  • Natalia Shenkman
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 190)

Abstract

The exchangeable d-variate wide-sense geometric law is uniquely characterized by (d + 1)-monotone sequences of parameters in [3]. The proof of sufficiency in [3] requires a probabilistic model. We provide an alternative, purely analytical proof of sufficiency of the (d + 1)-monotonicity of a sequence to define admissible parameters of a d-variate wide-sense geometric law.

Keywords

d-monotone sequences exchangeability lack of memory multivariate geometric law rectangular inequalities 

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References

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    Arnold, B.C.: A characterization of the exponential distribution by multivariate geometric compounding. Indian J. Stat. 37(1), 164–173 (1975)MATHGoogle Scholar
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    Joe, H.: Multivariate models and dependence concepts. Chapman & Hall (1997)Google Scholar
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    Mai, J.-F., Scherer, M., Shenkman, N.: Multivariate geometric distributions (logarithmically) monotone sequences, and infinitely divisible laws (working paper)Google Scholar
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    Ressel, P.: Monotonicity properties of multivariate distribution and survival functions with an application to Lévy-frailty copulas. J. Multivar. Anal. 102(3), 393–404 (2011)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jan-Frederik Mai
    • 1
  • Matthias Scherer
    • 2
  • Natalia Shenkman
    • 2
  1. 1.Assenagon Credit Managemant GmbHMünchenGermany
  2. 2.TU MunichGarching bei MünchenGermany

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