This paper proposes a test for the hypothesis that two samples have the same distribution. The likelihood ratio test of Portnoy (1988) is applied in the context of the consistent series density estimator of Crain (1974) and Barron and Sheu (1991). It is proven that the test, when suitably standardised, is asymptotically standard normal and consistent against any complementary alternative. In comparison with the established Kolmogorov-Smirnov and Cramer-von Mises procedures the proposed test enjoys broadly comparable finite sample size properties, but vastly superior power properties.
