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Multivariate geometric distributions, (logarithmically) monotone sequences, and infinitely divisible laws

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  • Mai, Jan-Frederik
  • Scherer, Matthias
  • Shenkman, Natalia

Abstract

Two stochastic representations of multivariate geometric distributions are analyzed, both are obtained by lifting the lack-of-memory (LM) property of the univariate geometric law to the multivariate case. On the one hand, the narrow-sense multivariate geometric law can be considered a discrete equivalent of the well-studied Marshall–Olkin exponential law. On the other hand, the more general wide-sense geometric law is shown to be characterized by the LM property and can differ significantly from its continuous counterpart, e.g., by allowing for negative pairwise correlations.

Suggested Citation

  • Mai, Jan-Frederik & Scherer, Matthias & Shenkman, Natalia, 2013. "Multivariate geometric distributions, (logarithmically) monotone sequences, and infinitely divisible laws," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 457-480.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:457-480
    DOI: 10.1016/j.jmva.2012.11.012
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    References listed on IDEAS

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    Cited by:

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    2. Mai, Jan-Frederik & Scherer, Matthias, 2020. "On the structure of exchangeable extreme-value copulas," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
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    4. Mai Jan-Frederik & Scherer Matthias, 2013. "What makes dependence modeling challenging? Pitfalls and ways to circumvent them," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 287-306, December.
    5. Shenkman, Natalia, 2017. "A natural parametrization of multivariate distributions with limited memory," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 234-251.

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