An investigation into the law of small numbers using R
Abstract
The Law of Small Numbers states that the Binomial distribution converges to the Poisson distribution. Using the programming language R, we investigate the total variation distance between Binomial(n, c/n) and Poisson(c) when we fix c and n individually. We also look at the asymptotics for ndTV for a fixed c, where ndTV is the total variation distance dTV multiplied by increasing values of n. Several properties of dTV are looked at in this paper.
Fields of Study & Subjects
Probability and Statistical Research
Statistical Distribution Estimation and Applications
Point processes and geometric inequalities
Publication details
- Journal / source
- Mathematics Exchange
- Volume
- 17
- Issue
- 1
- Pages
- 2–14
- Publication date
- 3 March 2026
- Language
- EN