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Measurements of separation among probability densities or random variables
Author(s) -
Glick Ned
Publication year - 1975
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315284
Subject(s) - pairwise comparison , mathematics , separation (statistics) , intuition , random variable , statistics , bayes' theorem , range (aeronautics) , pairwise independence , probability density function , statistical physics , sum of normally distributed random variables , multivariate random variable , bayesian probability , physics , philosophy , materials science , epistemology , composite material
Distance between two probability densities or two random variables is a well established concept in statistics. The present paper considers generalizations of distances to separation measurements for three or more elements in a function space. Geometric intuition and examples from hypothesis testing suggest lower and upper bounds for such measurements in terms of pairwise distances; but also in L p spaces some useful non‐pairwise separation measurements always lie within these bounds. Examples of such separation measurements are the Bayes probability of correct classification among several arbitrary distributions, and the expected range among several random variables.