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Inference in a bimodal Birnbaum–Saunders model

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  • Fonseca, Rodney V.
  • Cribari-Neto, Francisco

Abstract

We address the issue of performing inference on the parameters that index a bimodal extension of the Birnbaum–Saunders distribution (BS). We show that maximum likelihood point estimation can be problematic since the standard nonlinear optimization algorithms may fail to converge. To deal with this problem, we penalize the log-likelihood function. The numerical evidence we present shows that maximum likelihood estimation based on such penalized function is made considerably more reliable. We also consider hypothesis testing inference based on the penalized log-likelihood function. In particular, we consider likelihood ratio, signed likelihood ratio, score and Wald tests. Bootstrap-based testing inference is also considered. We use a nonnested hypothesis test to distinguish between two bimodal BS laws. We derive analytical corrections to some tests. Monte Carlo simulation results and empirical applications are presented and discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:146:y:2018:i:c:p:134-159
    DOI: 10.1016/j.matcom.2017.11.004
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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. Pianto, Donald M. & Cribari-Neto, Francisco, 2011. "Dealing with monotone likelihood in a model for speckled data," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1394-1409, March.
    3. Zhu, Xiaojun & Balakrishnan, N., 2015. "Birnbaum–Saunders distribution based on Laplace kernel and some properties and inferential issues," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 1-10.
    4. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    5. Wu, Jianrong & Wong, A. C. M., 2004. "Improved interval estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 809-821, November.
    6. Silvia Ferrari & Eliane Pinheiro, 2016. "Small-sample one-sided testing in extreme value regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(1), pages 79-97, January.
    7. Cribari-Neto, Francisco & Frery, Alejandro C. & Silva, Michel F., 2002. "Improved estimation of clutter properties in speckled imagery," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 801-824, October.
    8. 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.
    9. 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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