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

Abstract

This paper discusses the confidence sets estimation for the unit generalized Rayleigh distribution parameters when the record value is available. By constructing series of pivotal quantities, equal-tailed confidence intervals and region are constructed for unknown parameters. Further, optimal confidence sets with minimum-size are also pursued by using the non-linear optimization technique, whereas various numerical algorithms are also established to obtain the estimates in consequence. For comparison and complementary, traditional likelihood-based asymptotic confidence sets of the parameters are also constructed. Extensive simulation studies are carried out to evaluate the performance of different methods and two real-life examples are used to present their applicability. Additionally, some alternative extension works are also presented for pursuing high-accuracy confidence sets under proposed criteria and the effectiveness of the extended results is also investigated correspondingly.