Estimation of Pr (Y < X) for the Pareto Distribution

The Blackwell-Rao and Lehmann-Scheffé theorems are used to derive the minimum variance s-unbiased estimator of P ≡ Pr {Y < X} when the s-independent r.v.'s X and Y follow the 2-parameter Pareto distribution using censored samples. Estimators of P are also obtained using Bayesian and maximum likelihood methods. Performance of the three estimators for moderate samples is studied by Monte Carlo simulation.