Inference of record failure times from unit generalized Rayleigh distribution

Abstract

ABSTRACT In this paper, problems of estimation and prediction for record values are discussed for a two-parameter unit generalized Rayleigh distribution. Maximum likelihood estimators of model parameters along with their existence and uniqueness are established, and corresponding approximate confidence intervals are constructed based on asymptotic theory. In addition, alternative generalized inferential approach is provided for comparison based on the proposed pivotal quantities. Further, prediction intervals of remaining useful life are also presented under classical and generalized inferential methods when the unit generalized Rayleigh record values are available. Extensive numerical studies and two real-life examples are conducted to show the performance of the proposed methods. The results indicate that both classical and generalized estimation methods work satisfactorily and the proposed generalized inferential approach performs superior to traditional estimates in general.