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

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  • Ortega, Edwin M.M.
  • Cordeiro, Gauss M.
  • Lemonte, Artur J.

Abstract

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.

Suggested Citation

  • Ortega, Edwin M.M. & Cordeiro, Gauss M. & Lemonte, Artur J., 2012. "A log-linear regression model for the β-Birnbaum–Saunders distribution with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 698-718.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:698-718
    DOI: 10.1016/j.csda.2011.09.018
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    References listed on IDEAS

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    2. Leiva, Victor & Barros, Michelli & Paula, Gilberto A. & Galea, Manuel, 2007. "Influence diagnostics in log-Birnbaum-Saunders regression models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5694-5707, August.
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    2. Gauss Moutinho Cordeiro & Maria Do Carmo Soares De Lima & Edwin Moisés Marcos Ortega & Adriano Kamimura Suzuki, 2018. "A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications," Stats, MDPI, vol. 1(1), pages 1-16, May.
    3. Mahdi Teimouri, 2023. "Fast Bayesian Inference for Birnbaum-Saunders Distribution," Computational Statistics, Springer, vol. 38(2), pages 569-601, June.

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