Unified multivariate hypergeometric interpoint distances. Issue 4 (4th July 2019)

• Record Type: Journal Article
• Authors: Song, Yu; Modarres, Reza
• Is Part Of: Statistics. Volume 53:Issue 4(2019)
• Page Start: 921
• Page End: 942
• Publication Date: 2019-07-04
• Subjects: UMHG family -- interpoint distances -- norm -- mixture -- homogeneity; 62H10 -- 62E15 -- 62H15 -- 60E05; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2019.1618857
• Languages: English
• ISSNs: 0233-1888

Abstract

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 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.