Tables and Large-Sample Distribution Theory for Censored-Data Correlation Statistics for Testing Normality

References

• Abramowitz , M. and Stegun , I. A. 1964 . Handbook of Mathematical Functions , Washington , DC : National Bureau of Standards .
   Google Scholar
• Davies , R. B. 1980 . “The Distribution of a Linear Combination of χ 2 Random Variables,” . Applied Statistics , 38 : 52 – 73 .
   Google Scholar
• Davis , C. S. and Stephens , M. A. 1978 . “Approximating the Covariance Matrix of Normal Order Statistics,” . Applied Statistics , 27 : 206 – 212 .
   Google Scholar
• DeWet , T. and Venter , J. H. 1972 . “Asymptotic Distributions of Certain Test Criteria of Normality,” . South African Statistical Journal , 6 : 135 – 149 .
   Google Scholar
• DeWet , T. and Venter , J. H. 1973 . “Asymptotic Distributions for Quadratic Forms With Applications to Tests of Fit,” . The Annals of Statistics , 1 : 380 – 387 .
   Web of Science ®Google Scholar
• Filliben , J. J. 1975 . “The Probability Plot Correlation Coefficient Test for Normality,” . Technometrics , 17 : 111 – 117 .
   Web of Science ®Google Scholar
• Gerlach , B. 1980 . “A Correlation-Type Goodness-of-Fit Test for Normality With Censored Sampling,” . Mathematische Operationsforschung und Statistik , 11 : 207 – 218 . (Series Statistics)
   Google Scholar
• Gupta , A. K. 1952 . “Estimation of the Mean and Standard Deviation of a Normal Population From a Censored Sample,” . Biometrika , 39 : 260 – 273 .
   Web of Science ®Google Scholar
• Johnson , R. and Verrill , S. 1988 . “The Large Sample Distribution of the Shapiro—Wilk Statistic and Its Variations Under Type I and Type II Right Censoring,” unpublished manuscript
   Google Scholar
• Koziol , J. and Petkau , A. J. 1984 . “Relative Efficiencies of Goodness-of-Fit Procedures With Truncated Data,” . Canadian Journal of Statistics , 12 : 107 – 117 .
   Google Scholar
• Leslie , J. R. , Stephens , M. A. and Fotopoulos , S. 1986 . “Asymptotic Distribution of the Shapiro—Wilk W for Testing for Normality,” . The Annals of Statistics , 14 : 1497 – 1506 .
   Web of Science ®Google Scholar
• Mihalko , D. P. and Moore , D. S. 1980 . “Chi-Square Tests of Fit for Type II Censored Data,” . The Annals of Statistics , 8 : 625 – 644 .
   Web of Science ®Google Scholar
• Pettitt , A. N. 1976 . “Cramer—Von Mises Statistics for Testing Normality With Censored Samples,” . Biometrika , 63 : 475 – 481 .
   Web of Science ®Google Scholar
• Pettitt , A. N. and Stephens , M. A. 1976 . “Modified Cramer—Von Mises Statistics for Censored Data,” . Biometrika , 63 : 291 – 298 .
   Web of Science ®Google Scholar
• Rainville , E. D. 1960 . Special Functions , New York : Chelsea Publishing .
   Google Scholar
• Ryan , T. and Joiner , B. 1973 . “Normal Probability Plots and Tests for Normality,” , Pennsylvania State University, Dept. of Statistics . technical report
   Google Scholar
• Sarkadi , K. 1975 . “The Consistency of the Shapiro—Francia Test,” . Biometrika , 62 : 445 – 450 .
   Web of Science ®Google Scholar
• Shapiro , S. S. and Francia , R. A. 1972 . “An Approximate Analysis of Variance Test for Normality,” . Journal of the American Statistical Association , 67 : 215 – 216 .
   Web of Science ®Google Scholar
• Shapiro , S. S. and Wilk , M. B. 1965 . “Analysis of Variance Test for Normality (Complete Samples),” . Biometrika , 52 : 591 – 611 .
   Web of Science ®Google Scholar
• Shapiro , S. S. , Wilk , M. B. and Chen , H. J. 1968 . “A Comparative Study of Various Tests for Normality,” . Journal of the American Statistical Association , 63 : 1343 – 1372 .
   Web of Science ®Google Scholar
• Smith , R. M. and Bain , L. J. 1976 . “Correlation Type Goodness-of-Fit Statistics With Censored Sampling,” . Communications in Statistics, Part A—Theory and Methods , 5 : 119 – 132 .
   Web of Science ®Google Scholar
• Stephens , M. A. 1974 . “EDF Statistics for Goodness-of-Fit and Some Comparisons,” . Journal of the American Statistical Association , 69 : 730 – 737 .
   Web of Science ®Google Scholar
• Stephens , M. A. 1986 . “Tests Based on Regression and Correlation,” . In Goodness-of-Fit Techniques , Edited by: D'agostino , R. and Stephens , M. A. 195 – 233 . New York : Marcel Dekker .
   Google Scholar
• Verrill , S. P. 1981 . “Some Asymptotic Results Concerning Censored Data Versions of the Shapiro—Wilk Goodness of Fit Test,” , University of Wisconsin—Madison, Dept. of Statistics . unpublished Ph.D. dissertation
   Google Scholar
• Verrill , S. P. and Johnson , R. A. 1983 . “The Asymptotic Distributions of Censored Data Versions of the Shapiro—Wilk Test of Normality Statistic,” , University of Wisconsin—Madison, Dept. of Statistics . Technical Report 702
   Google Scholar
• Verrill , S. P. and Johnson , R. A. 1987a . “The Asymptotic Equivalence of Some Modified Shapiro-Wilk Statistics—Complete and Censored Sample Cases,” . The Annals of Statistics , 15 : 413 – 419 .
   Web of Science ®Google Scholar
• Verrill , S. P. and Johnson , R. A. 1987b . “A Large Sample Approximation to the Distribution of a Modified Shapiro—Wilk Statistic Under Right Censoring,” , Lawrence Livermore National Laboratory . UCRL-97603 preprint
   Google Scholar
• Weisberg , S. and Bingham , C. 1975 . “An Approximate Analysis of Variance Test for Non-normality Suitable for Machine Calculation,” . Technometrics , 17 : 133 – 134 .
   Web of Science ®Google Scholar