A few remarks on 'Statistical distribution of the difference of two proportions' by Nadarajah and Kotz, Statistics in Medicine 2007; 26(18):3518-3523.

摘要

Nadarajah and Kotz [1] derived an analytical expression for the statistical distribution of difference between two independent beta distributions. This result is useful for conducting exact Bayesian inference for risk difference between two populations. However, when we implemented this method, we found great discrepancies between the theoretical results based on their formula and simulation. Since the main contribution of Nadarajah and Kotz [1] is providing the distribution formula, we feel obligated to point out these mistakes and provide a corrected formula. In this short letter, we provide the corrected formula and conduct simulation to verify it.