Comparison of Different Estimators of P  [ Y  <  X ] for a Scaled Burr Type X Distribution

In this article, we consider the estimation of P[Y < X], when Y and X are two independent scaled Burr Type X distribution having the same scale parameters. The maximum likelihood estimator and its asymptotic distribution is used to construct an asymptotic confidence interval of P[Y < X]. Assuming that the common scale parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator, and approximate Bayes estimators of P[Y < X] are discussed. Different methods and the corresponding confidence intervals are compared using Monte Carlo simulations. One data set has been analyzed for illustrative purposes.