Smallest Confidence Region for Pareto Distribution Based on Records

In this article, a constrained optimization problem is formulated and solved in order to determine the smallest confidence region for the parameters of the Pareto distribution based on record values. We present some exact joint confidence regions for the parameters of the Pareto distribution based on record statistics. Using a linear interpolation, as well as numerical integration and optimization methods, some exact joint confidence regions for the parameters of the Pareto distribution based on record statistics are deduced. Finally, one numerical example as well as a simulation study, are given also to illustrate the methods proposed in this paper. It is shown that the reduction in area of the optimal confidence region with respect to the existing confidence regions is substantial.