M. Ya. Kelbert, Yu. M. Sukhov, “What scientific folklore knows about the distances between the most popular distributions”, Izv. Saratov Univ. Math. Mech. Inform., 2022, Volume 22, Issue 2,Pages <nobr>233

This article is cited in 1 paper

Scientific Part
Computer Sciences

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

M. Ya. Kelbert^a, Yu. M. Sukhov^bcd

^a Higher School of Economics – National Research University, 20 Myasnitskaya St., Moscow 101000, Russia
^b University of Cambridge, The Old Schools, Trinity Ln, Cambridge CB2 1TN, UK
^c University of Pennsylvania, 201 Old Main, State College, PA 16802, USA
^d Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 19 build. 1 Bolshoy Karetny per., Moscow 127051, Russia

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.

Key words: probability distribution, variation distance, Pinsker’s inequality, Le Cam’s inequalities, distances between distributions.

UDC: 519.85

Received: 25.11.2021
Accepted: 27.12.2021

Language: English

DOI: 10.18500/1816-9791-2022-22-2-233-240