Postprint version. Published in Annals of Institute of Statistical Mathematics, Volume 53, Issue 3, January 1, 2001, pages 543-551. Copyright © 2001 Institute of Statistical Mathematics, Tokyo. Published by Springer. The original publication is available at http://dx.doi.org/10.1023/A:1014673230617.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
A general goodness-of-fit test for scale-parameter families of distributions 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 exponentiality of data, compares favorably to other goodness-of-fit tests for exponentiality based on the empirical distribution function, regression methods and correlation 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).