Abstract
The normal distribution is among the most useful distributions in statistical applications. Accordingly, testing for normality is of fundamental importance in many fields including biopharmaceutical research. A generally powerful test for normality is the Shapiro-Wilk test, which can be derived based on estimated entropy divergence. Another well-known test for normality based on entropy divergence was proposed by Vasicek (1976) which has inspired the development of many goodness-of-fit tests for other important distributions. Despite extensive research on the subject, there still exists considerable confusion concerning the fundamental characteristics of Vasicek’s test. This article presents a unified derivation of both the Shapiro-Wilk test and Vasicek’s test based on estimated entropy divergence and clarifies some existing confusion. A comparative study of power performance for these two well-known tests for normality is presented with respect to a wide range of alternatives.