Evaluating the performance of modified Anderson–Darling goodness-of-fit tests for normality
Evaluating the performance of modified Anderson–Darling goodness-of-fit tests for normality

Summary/Abstract: The main aim of the article is to define and practically apply the modified Anderson– Darling (MAD) goodness-of-fit tests for normality. The modifications consist in varying the formula for calculating the empirical distribution function (EDF). Additional contributions of the paper include the expansion of the EDF family with four new proposals and the creation of a family of alternative distributions, consisting of both older and newer distributions that belong to all groups of skewness and kurtosis signs thanks to their flexibility. Critical values are obtained using 106 order statistics for sample sizes of n=10,20 and at a significance level of α=0.05. Finally, the article shows the calculation of the power of the analysed tests for alternative distributions based on 10^5 values of the test statistics. Their parameters have been selected to show several similarities to the normal distribution. The effectiveness of the tests is illustrated through the analysis of real datasets.

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