The limit distribution of a modified Shapiro–Wilk statistic for normality to Type II censored data

The Shapiro–Wilk statistic and modified statistics are widely used test statistics for normality. They are based on regression and correlation. The statistics for the complete data can be easily generalized to the censored data. In this paper, the distribution theory for the modified Shapiro–Wilk statistic is investigated when it is generalized to Type II right censored data. As a result, it is shown that the limit distribution of the statistic can be representable as the integral of a Brownian bridge. Also, the power comparison to the other procedure is performed.