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Extended Exponentiated Power Lindley Distribution

Author

Listed:
  • Ranjbar V.

    (Golestan University, Gorgan, Iran)

  • Alizadeh M.

    (Persian Gulf University, Bushehr, Iran)

  • Hamedani G. G.

    (Marquette University, Milwaukee, USA)

Abstract

In this study, we introduce a new model called the Extended Exponentiated Power Lindley distribution which extends the Lindley distribution and has increasing, bathtub and upside down shapes for the hazard rate function. It also includes the power Lindley distribution as a special case. Several statistical properties of the distribution are explored, such as the density, hazard rate, survival, quantile functions, and moments. Estimation using the maximum likelihood method and inference on a random sample from this distribution are investigated. A simulation study is performed to compare the performance of the different parameter estimates in terms of bias and mean square error. We apply a real data set to illustrate the applicability of the new model. Empirical findings show that proposed model provides better fits than other well-known extensions of Lindley distributions.

Suggested Citation

  • Ranjbar V. & Alizadeh M. & Hamedani G. G., 2018. "Extended Exponentiated Power Lindley Distribution," Statistics in Transition New Series, Statistics Poland, vol. 19(4), pages 621-643, December.
    • Handle: RePEc:vrs:stintr:v:19:y:2018:i:4:p:621-643:n:8
    DOI: 10.21307/stattrans-2018-033
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    References listed on IDEAS

    as
    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Wojciech Gamrot, 2013. "Maximum likelihood estimation for ordered expectations of correlated binary variables," Statistical Papers, Springer, vol. 54(3), pages 727-739, August.
    3. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    4. 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.
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