k-Sample tests based on the likelihood ratio

General k-sample tests are developed, including the classical Kolmogorov–Smirnov, Cramér–von Mises and Anderson–Darling k-sample tests, as well as new powerful omnibus tests based on the likelihood ratio. Conventional tests are sensitive to location difference among distributions, but are dull to detect the variation in shape. The new tests are sensitive to both location and shape. In fact, if the distributions of k-sampled populations are different in location only, the new tests are as powerful as the old ones. Otherwise, they are much more powerful.