Analysis of correlated Birnbaum-Saunders data based on estimating equations

Estimating equations for analyzing correlated Birnbaum-Saunders (BS) data are derived in this paper. A regression model is proposed for modeling the median of the life time until the failure, and a reweighted iterative process is developed for the joint estimation of the regression coefficients and the shape and correlation parameters. Diagnostic procedures, such as residual analysis and sensitivity studies based on case deletion and local influence, are given. Simulation studies are performed to assess the empirical distributions of the derived estimators and of a Pearson-type residual for correlated data. Finally, a longitudinal data set is analyzed by the procedures developed in the paper and extensions for the double case in which the median and the shape parameter are jointly modeled are discussed.