Point and interval estimation for the two-parameter Birnbaum–Saunders distribution based on Type-II censored samples

Abstract

The maximum likelihood estimators, based on Type-II censored samples, of a two-parameter Birnbaum–Saunders distribution are discussed. We propose a simple bias-reduction method to reduce the bias of the maximum likelihood estimators. We also discuss a Monte Carlo EM-algorithm for the determination of the maximum likelihood 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 these estimators are evaluated using Monte Carlo simulations for small, moderate, and large sample sizes, for various degrees of censoring. Two illustrative examples and some concluding remarks are finally presented.