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 which 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. The authors 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. Keywords: Goodness-of-fit, Normal order scores.

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Document Details

Document Type
Technical Report
Publication Date
Dec 22, 1988
Accession Number
ADA202269

Entities

People

  • J. R. Leslie
  • M. A. Stephens
  • S. Fotopoulos

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Analysis Of Variance
  • Consistency
  • Covariance
  • Data Science
  • Inequalities
  • Information Science
  • Military Research
  • New York
  • Normality
  • Numbers
  • Order Statistics
  • Probability
  • Statistical Samples
  • Statistics
  • Theorems
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Mathematics or Statistics
  • Statistical inference.