Abstract
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.
Highlights
Estimates of the closeness between probability distributions measured in terms of certain distances, the Kolmogorov and the total variation distances are very common in theoretical and applied probability
As far as we know, only a few exceptions deal with exact formulae
Denote by Sn(p) a random variable having the binomial distribution with parameters n and p, that is, P Sn(p) = k :=
Summary
Estimates of the closeness between probability distributions measured in terms of certain distances, the Kolmogorov and the total variation distances are very common in theoretical and applied probability. As far as we know, only a few exceptions deal with exact formulae (see, e.g., Kennedy and Quine [5], where the exact total variation distance between binomial and Poisson distributions is given for small values of the success parameter of the binomial). The aim of this note is to provide exact closed-form expressions for the Kolmogorov and the total variation distances between Poisson, binomial, and negative binomial distributions with different parameters.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
