The study of metrics in the space of probability measures and random elements has received wide attention and by now there is a wide variety of metrics available for study and use. In this review we discuss the interrelations between metrics of different type, the choice of an appropriate metric for a given approximation problem, the characterization of uniformities and compactness criteria for different metrics as well as applications of the theory of probability metrics to mass transportation problems, characterization of probability distributions and limit theorems for sums and maxima of random elements.
- Marshall-Olkin distribution
- characterization of probability distributions
- de Finetti's theorem
- mass transportation problems
- probability metrics
- quality usage
- stability of stochastic models