A Review of Distributional Testing Procedures and Development of a Censored Sample Distributional Test

A review of recent procedures for tests of distributional assumptions is given. Test procedures are grouped into three categories: regression type tests, probability integral transformation tests and special feature tests. The application of regression tests to distributions with location and shape parameters with emphasis on the normal, multivariate normal, exponential, and Weibull distributions and the advantages and limitations of recently improved EDF procedures are discussed. Tests which use characteristics unique to each of the normal, exponential, gamma, extreme value and Weibull distributions are also discussed.

[1]  James Durbin,et al.  Some methods of constructing exact tests , 1961 .

[2]  S. Shapiro,et al.  An Approximate Analysis of Variance Test for Normality , 1972 .

[3]  L. J. Ringer,et al.  Small Sample Power of Some Tests of the Constant Failure Rate , 1972 .

[4]  S. Shapiro,et al.  A Comparative Study of Various Tests for Normality , 1968 .

[5]  R. D'Agostino,et al.  Approaches to the null distribution of √ b1 , 1973 .

[6]  S. Kullback,et al.  Some Aspects of Multivariate Analysis. , 1958 .

[7]  Michael A. Stephens,et al.  Goodness of fit for the extreme value distribution , 1977 .

[8]  Ralph B. D'Agostino,et al.  Linear Estimation of the Weibull Parameters , 1971 .

[9]  A. Pettitt,et al.  Modified Cramér-von Mises statistics for censored data , 1976 .

[10]  A. Afifi,et al.  On Tests for Multivariate Normality , 1973 .

[11]  Oldrich A Vasicek,et al.  A Test for Normality Based on Sample Entropy , 1976 .

[12]  M. Stephens On the W Test for Exponentiality with Origin Known , 1978 .

[13]  J. Filliben The Probability Plot Correlation Coefficient Test for Normality , 1975 .

[14]  Boris Vladimirovič Gnedenko,et al.  Mathematical methods in the reliability theory , 1969 .

[15]  L. Shenton,et al.  Omnibus test contours for departures from normality based on √b1 and b2 , 1975 .

[16]  M. Stephens Tests of fit for the logistic distribution based on the empirical distribution function , 1979 .

[17]  E. S. Pearson,et al.  Tests for departure from normality. Empirical results for the distributions of b2 and √b1 , 1973 .

[18]  A. Pettitt Testing for bivariate normality using the empirical distribution function , 1979 .

[19]  Charles Locke,et al.  A test for the composite hypothesis that a population has a gamma distribution , 1976 .

[20]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[21]  M. Stephens EDF Statistics for Goodness of Fit and Some Comparisons , 1974 .

[22]  K. Sarkadi The consistency of the Shapiro—Francia test , 1975 .

[23]  G. J. Hahn,et al.  Statistical models in engineering , 1967 .

[24]  S. Shapiro,et al.  An Analysis of Variance Test for Normality (Complete Samples) , 1965 .

[25]  John R LaBrecque Goodness-of-Fit Tests Based on Nonlinearity in Probability Plots , 1977 .

[26]  F. David,et al.  Statistical Estimates and Transformed Beta-Variables. , 1960 .

[27]  N. Mann,et al.  A men goodness-of-fit test for the two-parameter wetbull or extreme-value distribution with unknown parameters , 1973 .

[28]  A note on testing for exponentiality , 1976 .

[29]  J. Durbin Kolmogorov-Smirnov tests when parameters are estimated with applications to tests of exponentiality and tests on spacings , 1975 .

[30]  M. B. Wilk,et al.  An Analysis of Variance Test for the Exponential Distribution (Complete Samples) , 1972 .

[31]  Michael A. Stephens,et al.  Asymptotic Results for Goodness-of-Fit Statistics with Unknown Parameters , 1976 .

[32]  H. Lilliefors On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown , 1967 .

[33]  A Test of Exponentiality Based on the Bivariate F Distribution , 1980 .

[34]  S. Weisberg An empirical comparison of the percentage points of W and W , 1974 .