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On Birnbaum-Saunders inference

Author

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  • Cysneiros, Audrey H.M.A.
  • Cribari-Neto, Francisco
  • Araújo Jr., Carlos A.G.

Abstract

The Birnbaum-Saunders distribution, also known as the fatigue-life distribution, is frequently used in reliability studies. We obtain adjustments to the Birnbaum-Saunders profile likelihood function. The modified versions of the likelihood function were obtained for both the shape and scale parameters, i.e., we take the shape parameter to be of interest and the scale parameter to be of nuisance, and then consider the situation in which the interest lies in performing inference on the scale parameter with the shape parameter entering the modeling in nuisance fashion. Modified profile maximum likelihood estimators are obtained by maximizing the corresponding adjusted likelihood functions. We present numerical evidence on the finite sample behavior of the different estimators and associated likelihood ratio tests. The results favor the adjusted estimators and tests we propose. A novel aspect of the profile likelihood adjustments obtained in this paper is that they yield improved point estimators and tests. The two profile likelihood adjustments work well when inference is made on the shape parameter, and one of them displays superior behavior when it comes to performing hypothesis testing inference on the scale parameter. Two empirical applications are briefly presented.

Suggested Citation

  • Cysneiros, Audrey H.M.A. & Cribari-Neto, Francisco & Araújo Jr., Carlos A.G., 2008. "On Birnbaum-Saunders inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4939-4950, July.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:11:p:4939-4950
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    References listed on IDEAS

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    1. Lemonte, Artur J. & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2007. "Improved statistical inference for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4656-4681, May.
    2. Steven E. Stern, 1997. "A Second‐order Adjustment to the Profile Likelihood in the Case of a Multidimensional Parameter of Interest," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 653-665.
    3. Ng, H. K. T. & Kundu, D. & Balakrishnan, N., 2003. "Modified moment estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 283-298, July.
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    1. Barreto, Larissa Santana & Cysneiros, Audrey H.M.A. & Cribari-Neto, Francisco, 2013. "Improved Birnbaum–Saunders inference under type II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 68-81.
    2. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    3. Azevedo, Cecilia & Leiva, Víctor & Athayde, Emilia & Balakrishnan, N., 2012. "Shape and change point analyses of the Birnbaum–Saunders-t hazard rate and associated estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3887-3897.
    4. Fonseca, Rodney V. & Cribari-Neto, Francisco, 2018. "Inference in a bimodal Birnbaum–Saunders model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 134-159.

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