smallest confidence region for pareto distribution based on records

In this article, a constrained optimization problem is formulated and solvedin order to determine the smallest confidence region for the parameters of the paretodistribution based on record values. we present some exact joint confidence regionsfor the parameters of the pareto distribution based on record statistics. using a linearinterpolation, as well as numerical integration and optimization methods, some exactjoint confidence regions for the parameters of the pareto distribution based on recordstatistics 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 thereduction in area of the optimal confidence region with respect to the existing confidenceregions is substantial.