Exact Kolmogorov and total variation distances between some familiar discrete distributions

By José A. Adell, Pedro Jodrá. 2006

67 citations recorded by the source corpus.

We give exact closed-form expressions for the Kolmogorov and the total variation distances between Poisson, binomial, and negative binomial distributions with different parameters. In the Poisson case, such expressions are related with the Lambert function.

Subfields: Applied Mathematics, Statistics and Probability

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In Applied Mathematics

1. Sanjiv Kumar
2. Felix X. Yu

In Statistics and Probability

1. Ananda Theertha Suresh
2. Sanjiv Kumar
3. Felix X. Yu
4. Yuhan Liu
5. Jakub Konecný
6. Vitaly Feldman
7. Peter Kairouz
8. Ji Liu

Citations in the corpus

• Learning discrete distributions: user vs item-level privacy (2020, background): “Furthermore, observe that By [Adell and Jodr´a, 2006, Proposition 2.3], for any two binomial distributions, , where (cid:100) m min( p, q (cid:48) ) (cid:101) ≤ k ≤ (cid:100) m max( p, q (cid:48) ) (cid:101) .”