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Interpoint distances: Applications, properties, and visualization
Author(s) -
Modarres Reza,
Song Yu
Publication year - 2020
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2508
Subject(s) - multivariate statistics , multidimensional scaling , cluster analysis , cumulative distribution function , mathematics , multivariate normal distribution , statistical physics , computer science , statistics , econometrics , probability density function , physics
This article surveys recent development on Euclidean interpoint distances (IPDs). IPDs find applications in many scientific fields and are the building blocks of several multivariate techniques such as comparison of distributions, clustering, classification, and multidimensional scaling. In this article, we explore IPDs, discuss their properties and applications, and present their distributions for several families, including the multivariate normal, multivariate Bernoulli, multivariate power series, and the unified hypergeometric distributions. We consider two groups of observations inR dand present a simultaneous plot of the empirical cumulative distribution functions of the within and between IPDs to visualize and examine the equality of the underlying distribution functions of the observations.