Estimation of p(y

We consider estimation of P(Y<X) when X˜Γr(M,λ) and Y˜Γ(N,μ) are independent with M and N known. A concise representation of the UMVUE and several representations for the MLE are derived. Closed-form exact expressions of both MSE's and the bias of the MLE are obtained. Large-sample results are given and numerical comparison of the two point estimators is made. Confidence intervals are given.