A log-linear regression model for the β -Birnbaum–Saunders distribution with censored data

• Published in: Computational statistics & data analysis Vol. 56; no. 3; pp. 698 - 718
• Main Authors: Ortega, Edwin M.M., Cordeiro, Gauss M., Lemonte, Artur J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2012
• Subjects: Birnbaum–Saunders distribution; Censored data; Crack propagation; Cure fraction; Data processing; Diagnostic systems; Generating function; Lifetime data; Mathematical analysis; Mathematical models; Maximum likelihood estimation; Regression; Regression model; Statistics; Survival; Censored data; Maximum likelihood estimation; Birnbaum–Saunders distribution; Generating function; Cure fraction; Regression model; Lifetime data
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2011.09.018

The β -Birnbaum–Saunders ( Cordeiro and Lemonte, 2011) and Birnbaum–Saunders ( Birnbaum and Saunders, 1969a) distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log- β -Birnbaum–Saunders distribution by the logarithm of the β -Birnbaum–Saunders distribution. Explicit expressions for its generating function and moments are derived. We propose a new log- β -Birnbaum–Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets.