An Analysis of Variance Test for the Exponential Distribution (Complete Samples)

Abstract

Procedures are developed for evaluation of various composite and simple hypotheses of exponentiality. The principles underlying these methods are similar to those used in 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.