Computing optimal confidence sets for Pareto models under progressive censoring

• Smallest-area joint confidence regions for the Pareto parameters are determined.
• The proposed procedure is valid for standard and progressive type II censoring.
• The reduction in area is substantial in most cases, and impressive sometimes.
• Shortest-length confidence intervals for the Pareto parameters are provided.
• Confidence bands for the Pareto reliability function may also be derived.

This paper presents two families of joint confidence sets for the Pareto shape and precision parameters based on progressively censored data, which include the existing regions in the literature as particular cases, and derives explicit expressions for the corresponding areas. Upon using fiducial arguments, an exact and quick computational method is then proposed in order to find the smallest-area Pareto region which depends on the minimal sufficient statistic with a specified confidence level. Shortest-length confidence intervals for the Pareto parameters are also provided. The reduction in area of the minimal joint confidence region with respect to the existing sets is substantial in most situations, and impressive in some cases. For illustrative and comparative purposes, two practical studies concerning device lifetimes and business failures are considered. Applications of the smallest confidence sets include uses in hypothesis testing and estimation. In particular, it is possible to construct confidence intervals for functions of the Pareto parameters, as well as pointwise and simultaneous confidence bands for the Pareto reliability function.