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Weighted inverse Gaussian -- a versatile lifetime model

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  • Ramesh C. Gupta
  • Debasis Kundu

Abstract

Jorgensen et al . [14] introduced a three-parameter generalized inverse Gaussian distribution, which is a mixture of the inverse Gaussian distribution and length biased inverse Gaussian distribution. Also Birnbaum--Saunders distribution is a special case for , where p is the mixing parameter. It is observed that the estimators of the unknown parameters can be obtained by solving a three-dimensional optimization process, which may not be a trivial issue. Most of the iterative algorithms are quite sensitive to the initial guesses. In this paper, we propose to use the EM algorithm to estimate the unknown parameters for complete and censored samples. In the proposed EM algorithm, at the M-step the optimization problem can be solved analytically, and the observed Fisher information matrix can be obtained. These can be used to construct asymptotic confidence intervals of the unknown parameters. Some simulation experiments are conducted to examine the performance of the proposed EM algorithm, and it is observed that the performances are quite satisfactory. The methodology proposed here is illustrated by three data sets.

Suggested Citation

  • Ramesh C. Gupta & Debasis Kundu, 2011. "Weighted inverse Gaussian -- a versatile lifetime model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2695-2708, February.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:12:p:2695-2708
    DOI: 10.1080/02664763.2011.567251
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    References listed on IDEAS

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    1. 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.
    2. Kundu, Debasis & Kannan, Nandini & Balakrishnan, N., 2008. "On the hazard function of Birnbaum-Saunders distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2692-2702, January.
    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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    Cited by:

    1. Jones, M.C., 2012. "Relationships between distributions with certain symmetries," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1737-1744.

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