Birnbaum-Saunders nonlinear regression models

TL;DR

This paper introduces a new class of Birnbaum-Saunders nonlinear regression models for lifetime data analysis, providing estimation methods, bias correction techniques, and demonstrating their effectiveness through simulations and real data application.

Contribution

It presents the first nonlinear regression models based on the Birnbaum-Saunders distribution, with explicit bias correction formulas and practical estimation procedures.

Findings

Bias correction yields nearly unbiased estimates.

Bias correction does not increase mean squared errors.

Models successfully applied to real fatigue data.

Abstract

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.