Modified moment estimation for the two-parameter Birnbaum–Saunders distribution

The maximum likelihood estimators and a modification of the moment estimators of a two-parameter Birnbaum–Saunders distribution are discussed. A simple bias-reduction method is proposed to reduce the bias of the maximum likelihood estimators and the modified moment estimators. The jackknife technique is also used to reduce the bias of these estimators. Monte Carlo simulation is used to compare the performance of all these estimators. The probability coverages of confidence intervals based on inferential quantities associated with all these estimators are evaluated using Monte Carlo simulations for small, moderate and large sample sizes. Two illustrative examples and some concluding remarks are finally presented.