Abstract
The empirical distribution function used in the classical Kolmogorov-Smirnov test invloving estimated parameters is redefined in such a way that it becomes a function of a parameter called delta. Simulation results for three important practical cases indicate that the size of the test is not affected by delta in the unit interval, and that power can be increased by as many as ten percentage points. A goodness of fit test procedure for the normal and exponential distributions with estimated parameters based in the mean and model plotting positions is proposed as a replacement to the classical Kolmogorov-Smirnov test.