 Multivariate Exponential and Geometric Distributions with Limited MemoryA. W. Marshall and I. Olkin Journal of Multivariate Analysis, 1995, vol. 53, issue 1, 110-125 Abstract: Many connections between geometric and exponential distributions are known. Characterizations and derivations of these distributions often run parallel. Moreover, one kind of distribution can be derived from the other: exponential distributions are limits of sequences of rescaled geometric distributions, and the integral parts of exponential random variables have geometric distributions. The lack of memory property is expressed by functional equations of the form (x + u) = (x) (u) for all (x, u) [set membership, variant] , where (x) = P{X1 > x1, ..., Xn > xn}. With = 2n+, the equation expresses a complete lack of memory that is possessed only by distributions with independent exponential marginals. But when is a proper subset of 2n+, the functional equation expresses a partial lack of memory property that in some cases is possessed by a more interesting family of multivariate exponential distributions, as for example, those with exponential minima. In this paper appropriate choices for and the resulting families of solutions are investigated, together with the associated families of multivariate geometric distributions. Date: 1995 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:53:y:1995:i:1:p:110-125 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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