A distribution free goodness of fit test for a stochastically ordered alternative

A distribution free goodness of fit test based on empirical distribution function is proposed for a one-sample and two-sample scenario under the alternative hypothesis of stochastic ordering. The exact and asymptotic null distribution of the proposed test statistic is derived. A Monte Carlo simulation study has been made to compare the power of the proposed test and other competitive test procedures. The proposed test performs better in the comparative study.