Inference of δ = P(X < Y) for Burr XII distributions with record samples.

Let X and Y follow independent Burr type XII distributions, which share a common inner shape parameter. The maximum likelihood estimator of the parameter δ = P(X < Y) is studied based on record samples. The existence and uniqueness of the maximum likelihood estimator of δ based on record samples are established. When the inner shape parameter is known, an exact confidence interval of δ is derived; otherwise, the Fisher information matrix and two bootstrap methods are used to obtain three approximate confidence intervals of δ. The performances of the proposed methods are evaluated via Monte Carlo simulation. Two examples are provided for illustration. [ABSTRACT FROM AUTHOR]