A log-Birnbaum-Saunders Regression Model with Asymmetric Errors

The paper by Leiva et al. (2010) introduced a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum-Saunders distribution associated with this distribution. In this paper, we introduce a skewed log-Birnbaum-Saunders regression model based on the skewed sinh-normal distribution. Some influence methods, such as the local influence and generalized leverage are presented. Additionally, we derived the normal curvatures of local influence under some perturbation schemes. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model.Comment: Submitted for publicatio

Small-sample corrections for score tests in Birnbaum-Saunders regressions

In this paper 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, the likelihood ratio test and its Bartlett-corrected version. Our simulation results suggest that the corrected test we propose is more reliable than the other tests.Comment: To appear in the Communications in Statistics - Theory and Methods, http://www.informaworld.com/smpp/title~content=t71359723

Robust Parameter Estimation in the Weibull and the Birnbaum-Saunders Distribution

This paper concerns robust parameter estimation of the two-parameter Weibull distribution and the two-parameter Birnbaum-Saunders distribution. We use the proposed method to estimate the distribution parameters from (i) complete samples with and without contamination (ii) type-II censoring samples, in both distributions. Also, we consider the maximum likelihood estimation and graphical methods to compare the maximum likelihood estimation and graphical method with the proposed method based on quantile. We find the advantages and disadvantages for those three different methods

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order $n^{-1/2}$ and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present an empirical application.Comment: Paper submitted for publication, with 13 pages and 1 figur