Integral Probability Metrics and Their Generating Classes of Functions

1997/06/01 by Alfred Müller · 11 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Probability and Risk Models #Probability and Statistical Research #Stochastic processes and financial applications

paper · doi:10.2307/1428011

crossref issued 1997/06/01 · crossref published 1997/06/01 · crossref published-print 1997/06/01 · openalex publication_date 1997/06/01 · crossref created 2006/04/23 · crossref published-online 2016/07/01 · crossref deposited 2019/05/11 · openalex created_date 2025/10/10 · crossref indexed 2026/07/29 · openalex updated_date 2026/07/30

Abstract

We consider probability metrics of the following type: for a class of functions and probability measures P, Q we define A unified study of such integral probability metrics is given. We characterize the maximal class of functions that generates such a metric. Further, we show how some interesting properties of these probability metrics arise directly from conditions on the generating class of functions. The results are illustrated by several examples, including the Kolmogorov metric, the Dudley metric and the stop-loss metric.

Citations

• Probability Metrics

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