A Comparative Study of Several One-Sided Goodness-of-Fit Tests

Abstract

Criteria for evaluating goodness-of-fit tests are reviewed and two additional criteria proposed. The several goodness-of-fit tests which have been proposed are studied in the light of these criteria. It is shown that it is relatively easy to evaluate the maximum and minimum power of those tests which are "partially ordered" against alternatives at a fixed "distance" from the hypothesis. A comparison is made of five tests on the basis of such minimum and maximum power functions.