An Information Theoretic Approach to Probability Mass Function Truncation

Given a discrete random variable X that takes values in a finite set χ according to a probability mass function (pmf) P, a truncated pmf Q of P is a conditional pmf that results from restricting the domain of X to some subset of χ. Truncated pmf arise in several problems of statistics and probability. In this paper, we propose and analyze a few criteria to truncate pmf's so that the truncated one is as much close as possible to the original pmf, under different information theoretic measures of distance.