Bootstrap-based improved estimators for the two-parameter Birnbaum–Saunders distribution

Abstract

In this paper, we consider the two-parameter Birnbaum–Saunders distribution proposed by Birnbaum and Saunders [Birnbaum, Z.W. and Saunders, S.C., 1969, A new family of life distributions. Journal of Applied Probability, 6, 319–327], which is commonly used for modeling the lifetime of materials and equipment. We consider different strategies of bias correction of the maximum-likelihood estimators for the parameters that index the distribution via bootstrap (parametric and nonparametric). The numerical evidence favors a particular bootstrap estimator based on parametric resampling. Finally, an example with real data is presented and discussed.