Estimation of δ = P(X < Y) for Burr XII distribution based on the progressively first failure-censored samples

Let X and Y have two-parameter Burr XII distributions. The maximum-likelihood estimator of delta = P(X < Y) is studied under the progressively first failure-censored samples. Three confidence intervals of d are constructed by using an asymptotic distribution of the maximum-likelihood estimator of d and two boot-strapping procedures, respectively. Some computational results from intensive simulations are presented. An illustrative example is provided to demonstrate the application of the proposed method.