On Birnbaum-Saunders Inference

TL;DR

This paper develops adjusted profile likelihood methods for the Birnbaum-Saunders distribution, improving inference on shape and scale parameters, with numerical evidence showing enhanced estimator and test performance.

Contribution

It introduces novel profile likelihood adjustments for Birnbaum-Saunders parameters, leading to better estimators and hypothesis tests in reliability analysis.

Findings

Adjusted estimators outperform traditional ones in finite samples

Modified likelihood ratio tests show improved accuracy

Adjustments are effective for both shape and scale parameter inference

Abstract

The Birnbaum-Saunders distribution, also known as the fatigue-life distribution, is frequently used in reliability studies. We obtain adjustments to the Birnbaum--Saunders profile likelihood function. The modified versions of the likelihood function were obtained for both the shape and scale parameters, i.e., we take the shape parameter to be of interest and the scale parameter to be of nuisance, and then consider the situation in which the interest lies in performing inference on the scale parameter with the shape parameter entering the modeling in nuisance fashion. Modified profile maximum likelihood estimators are obtained by maximizing the corresponding adjusted likelihood functions. We present numerical evidence on the finite sample behavior of the different estimators and associated likelihood ratio tests. The results favor the adjusted estimators and tests we propose. A novel aspect of the profile likelihood adjustments obtained in this paper is that they yield improved point estimators and tests. The two profile likelihood adjustments work well when inference is made on the shape parameter, and one of them displays superior behavior when it comes to performing hypothesis testing inference on the scale parameter. Two empirical applications are briefly presented.