A Note on Improved Approximation of the Binomial Distribution by the Skew-Normal Distribution

Abstract

It is a common practice to approximate a binomial distribution by a suitable normal distribution when n, the number of trials, is moderately large. But when p, the probability of success, is not close to 0.5, the binomial distribution can be heavily skewed, and hence the usual normal approximation may not be a good idea. In this note we show that the skew-normal distribution can provide a far better approximation due to its flexibility, and it can be used to approximate distributions other than the binomial one.