Small-Sample Corrections for Score Tests in Birnbaum–Saunders Regressions

Abstract

In this article, we deal with the issue of performing accurate small-sample inference in the Birnbaum–Saunders regression model, which can be useful for modeling lifetime or reliability data. We derive a Bartlett-type correction for the score test and numerically compare the corrected test with the usual score test and some other competitors.

Keywords:

• Bartlett-type correction
• Birnbaum–Saunders distribution
• Chi-square distribution
• Fatigue life distribution
• Lifetime data
• Likelihood ratio test
• Reliability data
• Score test

Mathematics Subject Classification:

• 62G10
• 62N05

Acknowledgments

We thank an anonymous referee for helpful suggestions which improved the article. We gratefully acknowledge grants from FAPESP and CNPq (Brazil).

Notes

LR _b  = LR/{1 + B(θ)/q}, where B(θ) is the Bartlett factor; see Lemonte et al. (2010) for details.

We used the approximation in (3) for a _{0, α} when α <0.5.