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Birnbaum–Saunders distribution based on Laplace kernel and some properties and inferential issues

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  • Zhu, Xiaojun
  • Balakrishnan, N.

Abstract

For the Birnbaum–Saunders distribution based on Laplace kernel, we discuss the shape characteristics of density and hazard functions. We show the existence and uniqueness of maximum likelihood estimates. Simple modified moment estimators are proposed and compared with maximum likelihood estimates.

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  • 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.
    • Handle: RePEc:eee:stapro:v:101:y:2015:i:c:p:1-10
    DOI: 10.1016/j.spl.2015.02.007
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    References listed on IDEAS

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    1. Barros, Michelli & Paula, Gilberto A. & Leiva, Víctor, 2009. "An R implementation for generalized Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1511-1528, February.
    2. Lemonte, Artur J. & Ferrari, Silvia L.P., 2011. "Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2388-2399, July.
    3. 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.
    4. Ng, H.K.T. & Kundu, D. & Balakrishnan, N., 2006. "Point and interval estimation for the two-parameter Birnbaum-Saunders distribution based on Type-II censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3222-3242, July.
    5. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, A., 2010. "Bivariate Birnbaum-Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 113-125, January.
    6. 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.
    7. Leiva, Victor & Riquelme, Marco & Balakrishnan, N. & Sanhueza, Antonio, 2008. "Lifetime analysis based on the generalized Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2079-2097, January.
    8. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    9. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, Ahad, 2013. "Generalized multivariate Birnbaum–Saunders distributions and related inferential issues," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 230-244.
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    Cited by:

    1. Fang, Longxiang & Zhu, Xiaojun & Balakrishnan, N., 2016. "Stochastic comparisons of parallel and series systems with heterogeneous Birnbaum–Saunders components," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 131-136.
    2. Longxiang Fang & N. Balakrishnan, 2018. "Ordering properties of the smallest order statistics from generalized Birnbaum–Saunders models with associated random shocks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 19-35, January.
    3. Xiaojun Zhu & N. Balakrishnan & Helton Saulo, 2019. "On the existence and uniqueness of the maximum likelihood estimates of parameters of Laplace Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 759-778, October.
    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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