Riedwyl-type test statistics for goodness-of-fit were introduced by Riedwyl in 1967, and generalized by Maag, Streit amp; Drouilly in 1973. In this paper these test statistics are extended for use in the case of discrete and grouped continuous data, with arbitrary grouping intervals. New Riedwyl-type test statistics are introduced, their distribution theory is discussed, and their power is compared with the power of the discrete Kolmogorov-Smirnov, Watson's, Kuiper's, and X2test statistics. The new statistics are shown to have greater power for particular alternatives.
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