Gibbs, Alison L.; Su, Francis Edward On choosing and bounding probability metrics. (English) Zbl 1217.62014 Int. Stat. Rev. 70, No. 3, 419-435 (2002). Summary: When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a means of deriving bounds for another one in an applied problem. Considering other metrics can also provide alternate insights. We also give examples that show that rates of convergence can strongly depend on the metric chosen. Careful consideration is necessary when choosing a metric. Cited in 247 Documents MSC: 62E10 Characterization and structure theory of statistical distributions 60B10 Convergence of probability measures 62E99 Statistical distribution theory PDFBibTeX XMLCite \textit{A. L. Gibbs} and \textit{F. E. Su}, Int. Stat. Rev. 70, No. 3, 419--435 (2002; Zbl 1217.62014) Full Text: DOI arXiv Link