On choosing and bounding probability metrics

Preprint

3 September 2002

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0209021

Abstract

When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by statisticians and probabilists. We focus on these metrics because they are either well-known, commonly used, or admit practical bounding techniques. We summarize these relationships in a handy reference diagram, and also give examples to show how rates of convergence can depend on the metric chosen.

Keywords

RATES OF CONVERGENCE
BOUNDING PROBABILITY
STUDYING CONVERGENCE
PROBABILITY METRIC
HANDY REFERENCE
ADMIT PRACTICAL
TEN IMPORTANT
METRICS

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Version 1, 2002-09-03, ArXiv

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