Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples

TL;DR

This paper develops and compares likelihood ratio and gradient tests for parameter inference in the Birnbaum-Saunders distribution with type-II censored data, demonstrating the gradient test's superiority through simulations and applications.

Contribution

It introduces a framework for hypothesis testing in censored Birnbaum-Saunders data using likelihood ratio and gradient statistics, highlighting the advantages of the gradient test.

Findings

Gradient test outperforms likelihood ratio test in finite samples.

Simulation results favor the gradient test for censored data.

Three real-world applications validate the proposed methods.

Abstract

The two-parameter Birnbaum-Saunders distribution has been used succesfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Three empirical applications are presented.