Parametric Estimation for the Birnbaum-saunders Lifetime Distribution Based on a New Parametrization

Abstract

In this article, we consider a new parametrization of the two-parameter Birnbaum-Saunders lifetime distribution. Importantly, this re-parametrization fits the physics of studying phenomena since the proposed parameters characterize or specify the thickness of the sample and the nominal treatment loading on the sample, respectively. The usual shape and scale parameters of the distribution do not offer this physical interpretation. Instead of substitution method of the parameter estimators of the original Birnbaum-Saunders model into the new model, the statistical properties of the direct application of the standard methods of point estimation to the new parameters are investigated. In an effort to appraise the performance of proposed estimators in a practical setting, Monte-Carlo simulations are conducted for small, moderate and large sample sizes. Two real life examples based on published data are used to illustrate the suggested estimation methods. Some concluding remarks and areas for further research are also presented.