  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.
