Estimation Methods for the Parameters of Birnbaum-Saunders Distribution

Abstract: Depending on the type of distribution, estimation of parameters are not sometimes simple in practice. In particular, this is the case for Birnbaum-Saunders distribution (BS). In this article, we present four different methods for estimating the parameters of a BS distribution. First, a simple graphical technique, analogous to probability plotting, is used to estimate the parameters and check for goodness-of-fit of failure times following a Birnbaum-Saunders distribution. Then, the maximum likelihood estimators and a modification of the moment estimators of a two-parameter Birnbaum–Saunders distribution are discussed. Finally, The jackknife technique is considered as another method which is appropriate for the small sample size case. Monte Carlo simulation is also used to compare the performance of all these estimators.