New Modified Anderson Darling Goodness of Fit Test for Lognormal and Gamma distributions

Abstract

The purpose of this study is to present the new modified Anderson-Darling goodness of fit test, and compare to the efficiency of three tests; Kolmogorov Smirnov test, Anderson-Darling test and Zhang (2002) test. A simulation study is used to estimate the critical values at a significance level of 0.05. The type I error rate and test power are calculated using Monte Carlo simulation with 10,000 replicates. The data are generated from the specified distribution; i.e., Lognormal and Gamma distributions with sample size of 10, 20, 30, 50, 100 and 200. The results demonstrate that every test has control over the type I error probability. The new test has the highest power for two alternative hypotheses; Loglogistic and Logistic distributions. Moreover, when the alternative distribution is Normal distribution and the sample size is small, the new test has the highest power.