Extreme-value Moment Goodness-of-fittests

A general goodness-of-fit test for scale-parameter families of distribu­ tions is introduced, which is based on quotients of expected sample minima. The test is independent of the mean of the distribution, and, in applications to testing for expQnentiality of data, compares favorably to other goodness-of-fit tests for expo­ nentialitybased on the empirical distribution function, regression methods and cor­ relation statistics. The new minimal-moment method uses ratios of easily-calculated, unbiased, strongly consistent U-statistics,and the general technique can be used to test many standard composite null hypotheses such as exponentiality, normality or uniformity (as well as simple null hypotheses).