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On choosing and bounding probability metrics

Alison L. Gibbs·Francis Edward Su
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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.

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Alison L. Gibbs, Francis Edward Su. 2002-09-03. On choosing and bounding probability metrics. https://arxiv.org/abs/math/0209021

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