Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/49919
Authors: 
Thadewald, Thorsten
Büning, Herbert
Year of Publication: 
2004
Series/Report no.: 
School of Business & Economics Discussion Paper: Economics 2004/9
Abstract: 
For testing normality we investigate the power of several tests, first of all, the well known test of Jarque and Bera (1980) and furthermore the tests of Kuiper (1960) and Shapiro and Wilk (1965) as well as tests of Kolmogorov-Smirnov and Cramer-von Mises type. The tests on normality are based, first, on independent random variables (model I) and, second, on the residuals in the classical linear regression (model II). We investigate the exact critical values of the Jarque-Bera test and the Kolmogorov-Smirnov and Cramer-von Mises tests, in the latter case for the original and standardized observations where the unknown parameters u and o have to be estimated. The power comparison is carried out via Monte Carlo simulation assuming the model of contaminated normal distributions with varying parameters u and o and different proportions of contamination. It turns out that for the Jarque-Bera test the approximation of critical values by the chi-square distribution does not work very well. The test is superior in power to its competitors for symmetric distributions with medium up to long tails and for slightly skewed distributions with long tails. The power of the Jarque-Bera test is poor for distributions with short tails, especially if the shape is bimodal, sometimes the test is even biased. In this case a modification of the Cramer-von Mises test or the Shapiro-Wilk test may be recommended.
Subjects: 
goodness-of-fit tests, tests of Kolmogorov-Smirnov and Cramervon Mises type, Shapiro-Wilk test, Kuiper test, skewness, kurtosis, contaminated normal distribution, Monte-Carlo simulation, critical values, power comparison
JEL: 
C12
C15
Document Type: 
Working Paper

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