A new approach of goodness-of-fit testing for exponentiated laws applied to the generalized Rayleigh distribution

Goodness-of-fit statistics are considered which are appropriate for generalized families of distributions, resulting from exponentiation. The tests employ a variation of the data determined by the cumulative distribution function of the corresponding non-generalized distribution. The resulting test, which makes use of the Mellin transform of the transformed data, is shown to be consistent. Simulation results for the case of the generalized Rayleigh distribution show that the proposed test compares well with standard methods based on the empirical distribution function.