Goodness-of-Fit Tests Based on Nonlinearity in Probability Plots

REFERENCES

• Anderson , T. W. and Darling , D. A. 1954 . A test of goodness of fit . J. Amer. Statist. Assoc. , 49 : 765 – 9 .
   Web of Science ®Google Scholar
• Borenious , G. 1966 . On the limit distribution of an extreme value in a sample from a normal distribution . Skand. Aktuarietidskr. , 1965 : 1 – 15 .
   Google Scholar
• Cramér , H. 1928 . On the composition of elementary errors . Skand. Aktuarietidskr. , 11 : 141 – 80 .
   Google Scholar
• David , F. N. and Johnson , N. L. 1954 . Statistical treatment of censored data. Part I. Fundamental formulae . Biometrika , 41 : 228 – 40 .
   Web of Science ®Google Scholar
• David , H. A. , Hartley , H. O. and Pearson , E. S. 1954 . The distribution of the ratio, in a single normal sample, of range to standard deviation . Biometrika , 41 : 482 – 93 .
   Web of Science ®Google Scholar
• Davies , O. L. , ed. 1956 . The Design and Analysis of Industrial Experiments. New York : Hafner. .
   Google Scholar
• Durbin , J. 1961 . Some methods of constructing exact tests . Biometrika , 48 : 41 – 55 .
   Web of Science ®Google Scholar
• Filliben , J. J. 1975 . The Probability Plot Correlation Test for Normality . Technomelrics , 17 : 111 – 17 .
   Web of Science ®Google Scholar
• Geary , R. C. 1935 . The ratio of the mean deviation of the standard deviation as a (new) test of normality . Biometrika , 27 : 310 – 32 .
   Google Scholar
• Govindarajula , Z. 1963 . On moments of order statistics and quasi-ranges from normal populations . Ann. Math. Statist. , 34 : 633 – 51 .
   Google Scholar
• Harter , H. L. 1961 . Expected values of normal order statistics . Biometrika , 48 : 151 – 65 .
   Web of Science ®Google Scholar
• Hildebrand , F. B. 1956 . Introduction to Numerical Analysis New York : McGraw-Hill. .
   Google Scholar
• Hogg , R. V. and Craig , A. T. 1956 . Sufficient statistics in elementary distribution theory . Sankhya , 17 : 209 – 16 .
   Google Scholar
• Kolmogorov , A. N. 1933 . Sulla determinazione empirica di one legge di distribuzione . S. Inst. Altuari , : 83 – 91 .
   Google Scholar
• Labrecque , J. F. 1973 . New goodness of fit procedures for the case of normality Buffalo : State University of New York. . Unpublished Ph.D. thesis
   Google Scholar
• Lilliefors , H. H. 1967 . On the Kolmogorov-Smirnov test for normality with mean and variance unknown . J. Amer. Statist. Assoc. , 62 : 399 – 402 .
   Web of Science ®Google Scholar
• Lloyd , E. H. 1952 . Least-squares estimation of location and scale parameters using order statistics . Biometrika , 39 : 88 – 95 .
   Web of Science ®Google Scholar
• Marsaglia , G. , Mclaren , M. D. and Bray , T. A. 1964 . A fast procedure for generating normal random variables . Comm. of the ACM , 7 : 4 – 10 .
   Web of Science ®Google Scholar
• Moore , D. S. 1968 . An elementary proof of asymptotic normality of linear functions of order statistics . Ann. Math. Statist. , 39 : 263 – 5 .
   Google Scholar
• Pearson , E. S. and Hartley , H. O. 1966 . Biometrika Tables for Statisticians., , 3rd Ed. Vol. 1 , Cambridge University Press. .
   Google Scholar
• Pearson , K. 1931 . On the mean character and variance of a ranked individual, and on the mean and variance of the intervals between ranked individuals . Biometrika , 23 : 364 – 97 .
   Google Scholar
• Sarhan , A. E. and Greenberg , B. G. , eds. 1959 . Contributions to Order Statistics. New York : Wiley. .
   Google Scholar
• Shapiro , S. S. 1964 . An Analyses of Variance Test for Normality , Ph.D. Thesis 45 – 48 . Rutgers University. . May 1964
   Google Scholar
• Shapiro , S. S. and Wilk , M. B. 1965 . An 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 . J. Amer. Statist. Assoc. , 63 : 1343 – 72 .
   Web of Science ®Google Scholar
• Stephens , M. A. 1974a . Asymptotic properties of covariance matrices for order statistics (To be published in Biometrika.)
   Google Scholar
• Stephens , M. A. 1974b . EDF statistics for goodness of fit with same comparisons (To be published in J. Amer. Statist. Assoc)
   Google Scholar
• Stigler , S. M. 1969 . Linear functions of order statistics . Ann. Math. Statist. , 40 : 770 – 88 .
   Google Scholar
• Wilks , S. S. 1962 . Mathematical Statistics New York : Wiley. .
   Google Scholar