**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series A, Pt. 3, pp. 464--472

**MODIFICATION OF SOME GOODNESS TO FIT STATISTICS II : TWO-SAMPLE AND SYMMETRY TESTING**

By

IBRAHIM A. AHMED, *Northern Illinois University*

SUMMARY. In recent article, Ahmed (1993), it was shown how the celebrated Cramér Von Mises and Watson statistics can be modified to yield asymptotically normal null distribution using the usual root n standardization. Her we continue along these lines and allow how such modification can be done in the two-sample case and in testing symmetry. These modified tests are consistent and distribution-free as well as equally applicable to the univariate or multivariate cases.

*AMS (1980) subject classification.* Primary 62F05.

*Key words and phrases.* Goodness of fit test, two-sample Cramer-von Mises statistics, testing for symmetry, power of tests.