Abstract
A new test of normality with unknown parameters is proposed in this article. We introduce a Cramér–von Mises type statistic with weight function equal to the inverse of the standard normal density function supported in the interval depending on the sample size n. The sequence is chosen so that the statistic goes to infinity and after subtracting the mean, a suitable test statistic is obtained, with the same asymptotic law as the well-known Shapiro–Wilk statistic. It is shown that the performance of the new test in many cases improves that of other well-known tests of normality.
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