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

Jan-Frederik Mai, Matthias Scherer and Natalia Shenkman

Journal of Multivariate Analysis, 2013, vol. 115, issue C, 457-480

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.

Keywords: Multivariate geometric law; Lack-of-memory; Exchangeability; Completely monotone sequence; De Finetti’s theorem; Infinitely divisible law (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.jmva.2012.11.012

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