A  Modified Anderson Darling Goodness of fit Test for the Generalized Rayleigh Distribution in the case where the parameters are estimated from the sample. Critical values are generated using a Monte Carlo simulation procedure with 10,000 repetitions each. Random samples of 10 different sizes were drawn from generalized Rayleigh distribution with different values of shape parameter. Fitted response functions for the critical values of based on the sample size and the shape parameter values are reported to avoid using a vest array of tables. This is followed by a power comparison using Monte Carlo methods at 5% and 1% significance levels for different sample size