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Procedures are developed for evaluation of various composite and simple hypotheses of exponentiality. The principles underlying these methods are similar to those used to defining and extending the W-statistic for normality (Shapiro and Wilk, 1965, 1968). The W-exponential statistic (scale and origin invariant) turns out to be the scaled ratio of the squared difference of the sample mean and smallest observation to the usual symmetric sum of squares about the mean. Procedures are developed to augment the W-exponential statistic when one or both of the location and scale parameters of the general exponential are specified. Necessary tables, some examples, and an abstract of an empirical sampling study of sensitivity are given. [ABSTRACT FROM AUTHOR]

Reports on the development of an approximation to the null distribution of a statistic suggested for the test of normality. Application of the results from an empirical sampling; Calculation of the moments of the ratio; Recommendation for the use of matching chosen percentage points.

Statistical methods are presented for the joint assessment of the supposed normality of a collection of independent (small) smaples, which may derive from populations having differing means and variances. The procedures are based on the use of the W statistic (Shapiiro and Wilk, 1965) as a measure of departure from normality. Two modes of combination of a collection of W statistics are considered, namely the standardized mean of the normal transforms of W and the sum of the χ[sup 2](2) transforms of the significance levels of W; and these are proposed for use in conjunction with the probability plotting of the collection of these transforms. Tables and formulae for practical implementation are provided. Some summary empirical sampling results are given on the comparative sensitivities of these procedures, along with detailed consideration of several specific examples which illustrate the additional information value of probability plotting. The proposed techniques appear to have susbtantial data analysis value as adjuncts to other statistical methodoloy. [ABSTRACT FROM AUTHOR]