Interval Estimation for the Shape and Scale Parameters of the Birnbaum—Saunders Distribution

Abstract

Two-parameter Birnbaum-Saunders distribution has been widely studied in Reliability Theory due to its important Engineering applications. This article proposes a novel confidence intervals construction for the shape and scale parameters of the Birnbaum-Saunders distribution. We apply the following two methods: The generalized pivotal approach and the percentile bootstrap approach. The Monte Carlo simulations are used to evaluate the performance of the confidence intervals. We compare the coverage probability and average width of the proposed confidence intervals with already known. Simulation results have shown that the proposed confidence intervals perform well in terms of coverage probability and average length for various sample sizes. The illustrative example and some concluding remarks are finally presented.