Unified multivariate hypergeometric interpoint distances

ABSTRACT

We establish (a) the probability mass function (p.m.f.) of the interpoint distance (IPD) between random vectors drawn from the unified multivariate hypergeometric (UMHG) family of distributions; (b) obtain the distribution of the IPD within one sample and across two samples from this family; (c) determine the distribution of the UMHG Euclidean norm and distance from fixed point in ${\mathbb{Z}}^d$; and (d) provide the distribution of the IPDs of vectors drawn from a mixture of the UMHG distribution. For application, we present a test the homogeneity of multivariate hypergeometric samples against mixture alternatives.

KEYWORDS:

• UMHG family
• interpoint distances
• norm
• mixture
• homogeneity

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62H10
• 62E15
• 62H15
• 60E05

Acknowledgements

We would like to thank three anonymous referees and the associate editor for constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.