Goodness of Fit Test Based on Modified Log-Likelihood Ratio for Normal Distribution
Abstract
This research presents a goodness of fit test based on modified log-likelihood ratio for normal distribution and compares the efficiency of the proposed test with modified Anderson-Darling test and modified Cramer-von-Mises test which were developed by Zhang (2002), and the original Anderson-Darling tests. The critical values of the tests are obtained through simulation and the efficiency of test is considered as probability of type I error and power of the tests. There are four types of distribution; near normal distribution, symmetric distribution, asymmetric distribution with more than three of kurtosis, and asymmetric distribution with less than three of kurtosis. The results show that the four tests can control type I error probability and the proposed test is the most powerful test for near normal and symmetric distributions with all sizes of sample. The modified Anderson-Darling test is the most powerful test for asymmetric distribution both more than three and less than three of kurtosis with all sizes of sample.
Keywords : goodness of fit test statistic, modified likelihood ratio , power of the test
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