A note on probability metrics in a categorical setting
Faculty of Sciences. Mathematics and Computer Science
Applied categorical structures. - Dordrecht, 1993, currens
, p. 1-9
University of Antwerp
Probability metrics constitute an important tool in probability theory and statistics (DallAglio et al. 1991; Rachev 1991; Zolotarev, Teor. Veroyatnost. i Primenen. 28(2), 2646, 1983) as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with the randomness structure. But probability metrics suffer from the same instability under constructions as metrics. In Lowen (2015), as well as in former and related work which can be found in the references of Lowen (2015), a comprehensive setting was developed to deal with this. It is the purpose of this note to point out that these ideas can also be applied to probability metrics thus embedding them in a natural categorical framework, showing that certain constructions performed in the setting of probability theory are in fact categorical in nature. This allows us to deduce various separate results in the literature from a unified approach.