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

Accepted - December 2022

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.