A Test For Normality Based On Entropy For Location-Scale Family Of Distributions With Applications To Box-Cox Transformations

Many statistical tests commonly used in practice assume that the distribution of the random observations is normal. Thus, the usual t-test and analysis of variance techniques belong to this category of statistical tests. While some of these statistical tests are robust to departures from this normality assumption, others are not. The most widely used confirmatory tests for normality include the Kolmogorov-Smirnov test, the chi-square goodness of fit test, Willks-Shapiro (Ryan-Joiner) test and the Anderson-Darling test. In this paper, we propose another test for normality based on the concept of entropy and show that it performs well in comparison with the above-mentioned tests, the Kolmogorov-Smirnov test in particular, in terms of power and its sensitivity to detect departures from the assumed normality. The entropy test is then applied to the determination of appropriate Box-Cox power transformations to normality