What scientific folklore knows about the distances between the most popular distributions

Abstract

We present a number of upper and low bounds for the total variation distances between the most popular probability distributions. In particular, some estimates of the total variation distances between one-dimensional Gaussian distributions, between two Poisson distributions, between two binomial distributions, between a binomial and a Poisson distribution, and also between two negative binomial distributions are given. The Kolmogorov – Smirnov distance is also presented.

Keywords

• probability distribution
• variation distance
• pinsker’s inequality
• le cam’s inequalities
• distances between distributions