Estimation of Scale Parameter and P(Y＜X) from Rayleigh Distribution

We consider the estimation problem for the scale parameter of the Rayleigh distribution using weighted balanced loss function (WBLF) which reflects both goodness of fit and precision. Under WBLF, we obtain the optimal estimator which creates a kind of balance between Bayesian and non-Bayesian estimation. We also deal with the estimation of R=P(Y＜X)when Y and X are two independent but not identically distributed Rayleigh distribution under squared error loss function.