Optimal Estimation of Confidence Set for a Bathtub-Shaped Lifetime Distribution under Records

In this paper, confidence set estimation is considered for the parameters from a bathtub-shaped lifetime distribution when record value is available. Based on proposed pivotal quantities, exact confidence intervals and confidence regions are established firstly for the model parameters. In addition, the corresponding optimal confidence intervals and confidence regions are also constructed by using Lagrange multiplier method under given significance level. Finally, simulation studies and a real life example are provided for illustration.