Goodness-of-Fit Tests for Grouped Data.

Following Riedwyl [8] we generalize some one-sample statistics of the Cramer-von Mises type so that they can be used to test grouped data for goodness of fit. We prove that under the null hypothesis the asymptotic distributions of these statistics, when suitably standardized, coincide with the corresponding classical statistics if the ratio of the sample size to the number of groups (k) remains constant. For k fixed the asymptotic distributions are given under the null hypothesis, and it is shown how to obtain them under any alternative. Some results for finite sample sizes are also derived, [ABSTRACT FROM AUTHOR]