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The Log-Linear Birnbaum-Saunders Power Model

Guillermo Martínez-Flórez (), Heleno Bolfarine () and Héctor W. Gómez ()
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Guillermo Martínez-Flórez: Universidad de Córdoba
Heleno Bolfarine: Universidade de São Paulo
Héctor W. Gómez: Universidad de Antofagasta

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 3, 913-933

Abstract: Abstract In this paper the sinh-power model is developed as a natural follow up to the log-linear Birnbaum-Saunders power model. The class of models resulting, incorporates the sinh-power-normal model, the ordinary sinh-normal model and the log-linear Birnbaum-Saunders model (Rieck and Nedelman, Technometrics 33:51–60, 1991). Maximum likelihood estimation is developed with the Hessian matrix used for standard error estimation. An application is reported for the data set on lung cancer studied in Kalbfleisch and Prentice (2002), where it is shown that the log-linear Birnbaum-Saunders power-normal model presents better fit than the log-linear Birnbaum-Saunders model. Another application is devoted to a fatigue data set previously analyzed in the literature. A nonlinear Birnbaum-Saunders power-normal model is fitted to the data set, with satisfactory performance.

Keywords: Birnbaum-saunders distribution; Fatigue life; Maximum likelihood; Power-normal; Sinh-power normal distribution; 60E05; 62F10; 62J05 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11009-016-9526-3

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