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

M. Y. Kelbert; Yu M. Suhov

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

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

M. Y. Kelbert, Yu M. Suhov

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English (US)
Pages (from-to)	233-240
Number of pages	8
Journal	Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
Volume	22
Issue number	2
DOIs	https://doi.org/10.18500/1816-9791-2022-22-2-233-240
State	Published - 2022

All Science Journal Classification (ASJC) codes

General Computer Science
Computational Mechanics
General Mathematics
Mechanics of Materials
Mechanical Engineering

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

Cite this

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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.",

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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