Estimations of Confidence Sets for the Unit Generalized Rayleigh Parameters Using Records Data

* Estimations of confidence sets are explored for the unit generalized Rayleigh distribution parameters with records data. Using the proposed pivotal quantities, equal-tailed confidence regions of the parameters are constructed. The associated optimal confidence sets with minimum-size are developed by non-linear optimization technique, and various numerical approaches are established for complex computations. For comparison and complementary, the likelihood asymptotic confidence sets of parameters are derived. Extensive simulation studies are conducted to evaluate the performance of all methods, and two practical examples are given for illustrations. Some alternative extensions are provided for pursuing potential higher accuracy confidence sets. Keywords: * unit generalized Rayleigh distribution; records data; confidence set estimation; pivotal quantity; nonlinear optimization.