Stein's Density Approach for Discrete Distributions and Information Inequalities

Abstract: We inscribe Stein's density approach for discrete distributionsin a new, exible framework, hereby extending and unifying a large portionof the relevant literature.We use this to derive a Stein identity whose powerwe illustrate by obtaining a wide variety of so-called inequalities betweenprobability metrics and information functionals. Whenever competitor in-equalities are available in the literature, the constants in ours are better.We also argue that our inequalities are local versions of the famous Pinskerinequality.