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

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Saratov, RF. 2022. Vol. 22. No. 2. P. 223–240.
Kelbert M., Suhov Y.

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.

Research target: Mathematics
Language: English
Full text
DOI
Keywords: Total variation distancePinsker inequalityLe Cam inequalities
Publication based on the results of:
Mathematical problems in the theory of evolution of biological systems and demography (2022)
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