Improved maximum likelihood estimation in Birnbaum–Saunders nonlinear regressions

We introduce, for the first time, a class of Birnbaum–Saunders nonlinear regression models. The new class of models 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 secondorder biases of these estimates. Our formulae are easily computed as ordinary linear regressions. The bias expressions are then used to define bias-corrected maximum likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates. We also give an application to a real data set.