2 research outputs found
Improved Likelihood Inference in Birnbaum-Saunders Regressions
The Birnbaum-Saunders regression model is commonly used in reliability
studies. We address the issue of performing inference in this class of models
when the number of observations is small. We show that the likelihood ratio
test tends to be liberal when the sample size is small, and we obtain a
correction factor which reduces the size distortion of the test. The correction
makes the error rate of he test vanish faster as the sample size increases. The
numerical results show that the modified test is more reliable in finite
samples than the usual likelihood ratio test. We also present an empirical
application.Comment: 17 pages, 1 figur
Birnbaum-Saunders nonlinear regression models
We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear
regression models potentially useful in lifetime data analysis. The class
generalizes the regression model described by Rieck and Nedelman [1991, A
log-linear model for the Birnbaum-Saunders distribution, Technometrics, 33,
51-60]. We discuss maximum likelihood estimation for the parameters of the
model, and derive closed-form expressions for the second-order biases of these
estimates. Our formulae are easily computed as ordinary linear regressions and
are then used to define bias corrected maximum likelihood estimates. Some
simulation results show that the bias correction scheme yields nearly unbiased
estimates without increasing the mean squared errors. We also give an
application to a real fatigue data set