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

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