The large sample distribution of the Shapiro--Wilk statistic and its variants under Type I or Type II censoring

The original Shapiro--Wilk statistic is extended for testing normality when the observations are Type I or Type II censored. We determine its large sample limit distribution under Type I or Type II censoring. This censored data limit distribution has an interesting relation to the complete sample solution and is obtained from it by replacing each Hermite polynomial with a censored data form. The same limit distribution also applies to several variants of the Shapiro--Wilk statistic which are related to the correlation coefficient associated with a normal probability plot.