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- W2001482661 abstract "A discussion about the estimators proposed by Zhang (1999) for the true standard deviation C of a normal distribution is presented. Those estimators, called by Zhang q 1 and q 2 , are functions of the expected values of the order statistics from a standard normal distribution and they were the basis of the Q statistic used in the derivation of a new test for normality proposed by Zhang. Although the type I error and the power of the test was discussed by Zhang, no study was performed to test the reliability of q 1 and q 2 as estimators of C . In this paper, it is shown that q 1 is a very poor estimator for C especially when C is large. On the other hand, the estimator q 2 has a performance very similar to the well-known sample standard deviation S. When some correlation is introduced among the sample units it can be seen that the estimator q 1 is much more affected than the estimators q 2 and S." @default.
- W2001482661 created "2016-06-24" @default.
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- W2001482661 date "2003-04-01" @default.
- W2001482661 modified "2023-09-24" @default.
- W2001482661 title "A note on the Zhang omnibus test for normality based on the Q statistic" @default.
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- W2001482661 doi "https://doi.org/10.1080/0266476022000030101" @default.
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