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Generalized logistic frailty model

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  • Lai, Chin-Diew
  • Izadi, Muhyiddin

Abstract

We propose a new reliability model which is a generalization of the logistic frailty model first considered by Vaupel (1990) for fitting human mortality data. Essentially, a shape parameter is added to the existing model providing more flexibility in modeling lifetime data. Several model properties such as the survival function, density and the hazard rate are investigated. In particular, we show that the model is very versatile; able to take a variety of non-monotonic hazard rate shapes. Parameters estimation is also considered. Two well known survival data sets are satisfactorily fitted by the proposed distribution and its goodness-of-fit is compared.

Suggested Citation

  • Lai, Chin-Diew & Izadi, Muhyiddin, 2012. "Generalized logistic frailty model," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1969-1977.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1969-1977
    DOI: 10.1016/j.spl.2012.06.012
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    References listed on IDEAS

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    1. Maxim S. Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," MPIDR Working Papers WP-2009-031, Max Planck Institute for Demographic Research, Rostock, Germany.
    2. Anatoli Yashin & Ivan Iachine & Alexander Begun, 2000. "Mortality modeling: A review," Mathematical Population Studies, Taylor & Francis Journals, vol. 8(4), pages 305-332.
    3. Maxim Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 643-663, November.
    4. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
    5. Jiang, R. & Murthy, D.N.P., 2009. "Impact of quality variations on product reliability," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 490-496.
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    Cited by:

    1. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.

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