On the Normal Approximation for Some Special Estimators of the Ratio of Binomial Proportions

We focus on the normal approximation for special cases of point estimators of the ratio of Binomial proportions of two independent populations. We prove that these estimators are normally distributed, something that has not been done before. We investigate its performance in terms of bias, variance, and mean square error, using Monte Carlo simulations. The results show that the normal approximation, which is relatively simple, provides a reliable result. The normal approximation approach could be recommended on the basis of the specific values of the parameters and/or sample sizes.