We establish (a) the probability mass function of the interpoint distance (IPD) between random vectors that are drawn from the multivariate power series family of distributions (MPSD); (b) obtain the distribution of the IPD within one sample and across two samples from this family; (c) determine the distribution of the MPSD Euclidean norm and distance from fixed points in \({\mathbb {Z}}^d\); and (d) provide the distribution of the IPDs of vectors drawn from a mixture of the MPSD distributions. We present a method for testing the homogeneity of MPSD mixtures using the sample IPDs.

中文翻译：

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多元幂级数点间距离

我们建立（a）从多元幂级数分布族（MPSD）得出的随机向量之间的点间距离（IPD）的概率质量函数；（b）获得IPD在该家庭的一个样本中以及在两个样本中的分布；（c）确定MPSD欧几里得范数的分布以及距\（{\ mathbb {Z}} ^ d \）中的固定点的距离；（d）提供从MPSD分布的混合中得出的矢量的IPD分布。我们提出了一种使用样本IPD测试MPSD混合物均匀性的方法。