A constrained optimization problem for determining the smallest Pareto confidence region under progressive Type-II censoring

In this paper, a constrained optimization problem is formulated and solved to determine the smallest joint confidence region for Pareto parameters based on the progressively Type-II censored samples. The objective function is the area of the confidence region and the problem constraint is the specified confidence level. The proposed joint confidence ‎region is also valid for the complete samples and right censored samples. The area of the smallest proposed confidence region and the area of the balanced confidence region are compared. Finally, two numerical examples are presented to describe the proposed optimization method.