Some Applications of Exponential Ordered Scores

Summary There are simple standard tests for the comparison of samples assumed to arise from exponential distributions, but the properties of these tests are known to depend severely on the assumption of exponential form. However, the observations can sometimes usefully be ranked, and then replaced by the corresponding expected values of order statistics in sampling the unit exponential distribution, before calculating the appropriate test statistic. Some special tests of this type are examined. The procedure is analogous to the use of Fisher and Yates's scores in normal theory. Savage (1956) gave the test of this type for comparing two samples, in the course of a general study of rank tests for the two-sample problem.