论文标题
多变量几何分布，（对数）单调序列和无限划分的定律（由Natalia Shenkman的勘误）
Multivariate geometric distributions, (logarithmically) monotone sequences, and infinitely divisible laws (with erratum by Natalia Shenkman)
论文作者
论文摘要
分析了多元几何分布的两个随机表示，这两者都是通过提高单变量几何定律的缺乏记忆（LM）特性来获得多变量情况的。一方面，狭窄的多元几何定律可以被视为与经过良好研究的Marshall-Olkin指数定律相当的离散。另一方面，更一般的宽宽几何定义法被证明具有LM特性的特征，并且可以通过允许负成对相关性来与其连续的对应物有显着差异。 对于这两个分布式的家族，其$ d $二维交换子类的特征是通过$ d $ -log-Monotone，resp。\ $ d $ - 单酮，参数序列。使用这种重新聚集化，根据De Finetti定理的意义，分布的亚家族具有条件性I.I.D. \组件。为此，提出了基于非降低随机步行的第三个随机结构。当相关随机步行的增量无限分区时，狭窄的家族就会嵌入这种结构中。此外，可交换狭窄的定律还显示出具有多元右尾巴增加（MRTI）的依赖性。
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. For both families of distributions, their $d$-dimensional exchangeable subclass is characterized analytically via $d$-log-monotone, resp.\ $d$-monotone, sequences of parameters. Using this reparameterization, the subfamilies of distributions with conditionally i.i.d.\ components in the sense of de Finetti's theorem are determined. For these, a third stochastic construction based on a non-decreasing random walk is presented. The narrow-sense family is embedded in this construction when the increments of the involved random walk are infinitely divisible. The exchangeable narrow-sense law is furthermore shown to exhibit the multivariate right tail increasing (MRTI) dependence.
