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A Three-Parameter Weighted Lindley Distribution and its Applications to Model Survival Time

Author

Listed:
  • Shanker Rama

    (Department of Statistics, Eritrea Institute of Technology, Asmara, Eritrea)

  • Shukla Kamlesh Kumar

    (Department of Statistics, Eritrea Institute of Technology, Asmara, Eritrea)

  • Mishra Amarendra

    (Department of Statistics, Patna University, Patna, India)

Abstract

In this paper a three-parameter weighted Lindley distribution, including Lindley distribution introduced by Lindley (1958), a two-parameter gamma distribution, a two-parameter weighted Lindley distribution introduced by Ghitany et al. (2011) and exponential distribution as special cases, has been suggested for modelling lifetime data from engineering and biomedical sciences. The structural properties of the distribution including moments, coefficient of variation, skewness, kurtosis and index of dispersion have been derived and discussed. The reliability properties, including hazard rate function and mean residual life function, have been discussed. The estimation of its parameters has been discussed using the maximum likelihood method and the applications of the distribution have been explained through some survival time data of a group of patients suffering from head and neck cancer, and the fit has been compared with a one-parameter Lindley distribution and a two-parameter weighted Lindley distribution.

Suggested Citation

  • Shanker Rama & Shukla Kamlesh Kumar & Mishra Amarendra, 2017. "A Three-Parameter Weighted Lindley Distribution and its Applications to Model Survival Time," Statistics in Transition New Series, Statistics Poland, vol. 18(2), pages 291-310, June.
    • Handle: RePEc:vrs:stintr:v:18:y:2017:i:2:p:291-310:n:3
    DOI: 10.21307/stattrans-2016-071
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    References listed on IDEAS

    as
    1. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
    2. Ghitany, M.E. & Alqallaf, F. & Al-Mutairi, D.K. & Husain, H.A., 2011. "A two-parameter weighted Lindley distribution and its applications to survival data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1190-1201.
    3. A. Mishra & R. Shanker, 2013. "A two-parameter Lindley distribution," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 14(1), pages 45-56, March.
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