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Convergence of Binomial to Poisson Distribution (An Empirical Approach)

Binomial and poisson distributions have numerous applications in probability and statistics. According to a limit theorem, when n tends to infinity and p to zero, while rip remains constant, the binomial tends to the poisson distribution. But in practice, it is impossible to have a case in which n tends to infinity or p to zero. Therefore, in this article, we identify the situations for n and p such that the difference between the binomial and poisson distributions is negligible according to the root of MSE criterion. In such settings, we can use poisson as an approximation to binomial distribution.