Recent results on the total variation distance

Abstract

Let (X 1 ,...,X n ) and (Y 1 ,...,Y n ) be two sets of independent discrete random variables. Explicit upper and lower bounds for the total variation distance between distributions of these sets are obtained in terms of some functions of distributions of separate components X k and Y k , k = 1,...,n. The cases of identical (inside each set) and arbitrary distributions of random variables are considered. Results may be used to estimate the sample sizes necessary or sufficient for testing two hypotheses with given sum of error probabilities.