The Kolmogorov-Smirnov, Cramer-von Mises Tests

Preface. This is an expository paper giving an account of the goodness of fit test and the two sample test based on the empirical distribution functiontests which were initiated by the four authors cited in the title. An attempt is made here to give a fairly complete coverage of the history, development, present status, and outstanding current problems related to these topics. The reader is advised that the relative amount of space and emphasis allotted to the various phases of the subject does not reflect necessarily their intrinsic merit and importance, but rather the author's personal interest and familiarity. Also, for the sake of uniformity the notationt of miany of the writers quoted has been altered so that when referring to the original papers it will be necessary to check their nomenlclature. 2. The empirical distribution function and the tests. Let XI, X2, * * ,XXn be independent random variables (observations) each having the same distribution