Inference on the parameters of the Weibull distribution using records

Abstract

The Weibull distribution is a very applicable model for lifetime data. In this paper, we have investigated inference on the parameters of Weibull distribution based on record values. We first propose a simple and exact test and a confidence interval for the shape parameter. Then, in addition to a generalized confidence interval, a generalized test variable is derived for the scale parameter when the shape parameter is unknown. The paper presents a simple and exact joint confidence region as well. In all cases, simulation studies show that the proposed approaches are more satisfactory and reliable than previous methods. All proposed approaches are illustrated using a real example.