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An Analytical Characterization of the Exchangeable Wide-Sense Geometric Law

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Synergies of Soft Computing and Statistics for Intelligent Data Analysis

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 190))

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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.

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References

  1. Arnold, B.C.: A characterization of the exponential distribution by multivariate geometric compounding. Indian J. Stat. 37(1), 164–173 (1975)

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  2. Joe, H.: Multivariate models and dependence concepts. Chapman & Hall (1997)

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  3. Mai, J.-F., Scherer, M., Shenkman, N.: Multivariate geometric distributions (logarithmically) monotone sequences, and infinitely divisible laws (working paper)

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  4. 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)

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Author information

Authors and Affiliations

  1. Assenagon Credit Managemant GmbH, 80339, München, Germany

    Jan-Frederik Mai

  2. TU Munich, 85748, Garching bei München, Germany

    Matthias Scherer & Natalia Shenkman

Authors
  1. Jan-Frederik Mai
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  2. Matthias Scherer
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  3. Natalia Shenkman
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Corresponding author

Correspondence to Jan-Frederik Mai .

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Otto-von-Guericke University of Magdebur, Geb. 29, Raum 008, Universitätsplatz 2, Magdeburg, 39106, Germany

    Rudolf Kruse

  2. , FB Informatik & Informationswissenschaft, University of Konstanz, Konstanz, 78457, Germany

    Michael R. Berthold

  3. of Magdeburg, Faculty of Computer Science, Otto-von-Guericke University, Geb. 29, Universitätsplatz 2 008, Magdeburg, 39106, Germany

    Christian Moewes

  4. , Department of Statistics and OR, University of Oviedo, C/ Calvo Sotelo, s/n, Oviedo, 33007, Spain

    María Ángeles Gil

  5. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Przemysław Grzegorzewski

  6. Systems Research Institute, Polish Academy of Sciences, Newelska 6, Warsaw, 01-447, Poland

    Olgierd Hryniewicz

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Mai, JF., Scherer, M., Shenkman, N. (2013). An Analytical Characterization of the Exchangeable Wide-Sense Geometric Law. In: Kruse, R., Berthold, M., Moewes, C., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33042-1_36

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  • DOI: https://doi.org/10.1007/978-3-642-33042-1_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33041-4

  • Online ISBN: 978-3-642-33042-1

  • eBook Packages: EngineeringEngineering (R0)

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