## The Annals of Statistics

### Asymptotic Distribution of the Shapiro-Wilk $W$ for Testing for Normality

#### Abstract

Twenty years have elapsed since the Shapiro-Wilk statistic $W$ for testing the normality of a sample first appeared. In that time a number of statistics that are close relatives of $W$ have been found to have a common (known) asymptotic distribution. It was assumed, therefore, that $W$ must have that asymptotic distribution. We show this to be the case and examine the norming constants that are used with all the statistics. In addition the consistency of the $W$ test is established.

#### Article information

Source
Ann. Statist., Volume 14, Number 4 (1986), 1497-1506.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350172

Digital Object Identifier
doi:10.1214/aos/1176350172

Mathematical Reviews number (MathSciNet)
MR868314

Zentralblatt MATH identifier
0622.62019

JSTOR
Leslie, J. R.; Stephens, M. A.; Fotopoulos, S. Asymptotic Distribution of the Shapiro-Wilk $W$ for Testing for Normality. Ann. Statist. 14 (1986), no. 4, 1497--1506. doi:10.1214/aos/1176350172. https://projecteuclid.org/euclid.aos/1176350172