Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Kelbert M. Y., Suhov Y. M. What scientific folklore knows about the distances between the most popular distributions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 2, pp. 233-240. DOI: 10.18500/1816-9791-2022-22-2-233-240

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.05.2022
Full text:
(downloads: 471)
Language: 
English
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Article type: 
Article
UDC: 
519.85

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

Autors: 
Kelbert Mark Yakovlevich, Higher School of Economics – National Research University
Suhov Yurii M., University of Cambridge
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.

References: 
  1. Suhov Yu., Kelbert M. Probability and Statistics by Example. Vol. I. Basic Probability and Statistics. 2nd ed. Cambridge, UK, Cambridge University Press, 2014. 470 p. https://doi.org/10.1017/CBO9781139087773  
  2. Pinsker M. Information and Information Stability of Random Variables and Processes. San Francisco, USA, Holden-Day Inc., 1964. 243 p.
  3. Le Cam L. Asymptotic Methods in Statistical Decision Theory. Springer Series in Statistics. New York, NY, Springer, 1986. 742 p. https://doi.org/10.1007/978-1-4612-4946-7
  4. Le Cam L. An approximation theorem for the Poisson binomial distribution. Pacific Journal of Mathematics, 1960, vol. 10, no. 4, pp. 1181–1197. https://doi.org/10.2140/pjm.1960.10.1181
  5. Devroye L., Mehrabian A., Reddad T. The total variation distance between high-dimensional Gaussians. ArXiv, 2020, ArXiv:1810.08693v5, pp. 1–12.
Received: 
25.11.2021
Accepted: 
27.12.2021
Published: 
31.05.2022