Abstract
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.
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