Suppose X follows Rayleigh (theta1) and Y has Rayleigh (theta2) then R=P(X>Y) can be estimated by MLE after writing the joint likelihood function of independent variables X and Y. So my question is that, is it possible to obtain the least square estimator or Maximum product spacing estimator of R, (by using invariance property) after estimation of theta1 and theta2 for both the independent random variables X and Y separately, because jointly estimation as in case of MLE is not possible in such methods. Or is it possible here because the model under study have no common parameter.