Some New Goodness-of-Fit Tests Based on Stochastic Sample Quantiles

This article introduces some new tests for goodness-of-fit based on the differences between the sample quantiles and stochastic sample quantiles derived from the null distribution. Because stochastic sample quantiles for given sample observations are random, randomized statistics are derived, of which the qth quantile and the expectation are chosen as test statistics. Under uniform hypothesis, the asymptotic distributions of some new test statistics are given, respectively. The powers of the new tests under certain alternatives are examined. They are more powerful tests for the hypotheses concerned.