May 30, 2006 13:2 Journal of Statistical Computation & Simulation bs2˙jscs˙v2 Journal of Statistical Computation & Simulation Vol. 00, No. 00, Month 200x, 1–20 Bootstrap-based improved estimators for the two-parameter Birnbaum-Saunders distribution ARTUR J. LEMONTE, ALEXANDRE B. SIMAS and FRANCISCO CRIBARI-NETO * Departamento de Estat´ ıstica, Universidade Federal de Pernambuco, Cidade Universit´aria, Recife/PE, 50740-540, Brazil (Received 00 Month 200x; In final form 00 Month 200x) In this paper, we consider the two-parameter Birnbaum-Saunders distribution proposed by Birn- baum and Saunders [Birnbaum, Z.W. and Saunders, S.C., 1969a, A new family of life distributions. Journal of Applied Probability , 6, 319–327], which is commonly used for modeling the lifetime of materials and equipments. 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. Keywords: Bootstrap; Bias correction; Birnbaum-Saunders distribution; Maximum likelihood estimation. 1 Introduction Birnbaum and Saunders [1] proposed a new family of life distributions for modeling the lifetime of materials and equipments under the influence of dy- namic loads. This two-parameter Birnbaum-Saunders distribution was derived from a model in which failures happen due to the development and growth of a dominant crack. Later, this distribution was derived in a more general way by Desmond [3], based on a biological model. Desmond also extended the physical justification for its use by relaxing some of the assumptions made in Birnbaum and Saunders [1]. Moreover, Desmond [4] investigated the relation- ship between the Birnbaum-Saunders distribution and the inverse Gaussian distribution. A random variable T is said to follow the two-parameter Birnbaum-Saunders distribution with parameters α, β > 0, denoted by B-S (α, β), if its cumulative * Corresponding author. Email: cribari@de.ufpe.br