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 nd_TV for a fixed c, where nd_TV is the total variation distance d_TV multiplied by increasing values of n. Several properties of d_TV are looked at in this paper.

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Recommended citation: Barlas, Y., Stark, D. (2023), “An investigation into the law of small numbers using R”, Ball State Undergraduate Mathematics Exchange, 17(1):2-14