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Lindley–Exponential distribution: properties and applications

Author

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  • Deepesh Bhati
  • Mohd. Malik
  • H. Vaman

Abstract

In this paper, we introduce a new class of distributions generated by an integral transform of the probability density function of the Lindley distribution which results in a model that is more flexible in the sense that the derived model spans distributions with increasing failure rate, decreasing failure rate and upside down bathtub shaped hazard rate functions for different choices of parametric values. For this new model, various distributional properties including limiting distribution of extreme order statistics are established. Maximum likelihood estimators and the marginal confidence intervals of the parameters are obtained. The applicability of the proposed distribution is shown through application to real data sets. Through application to two real datasets, it is demonstrated that the proposed model fits better as compared to some other competing models. Further, the model is shown to be useful for analysing stress–strength model. Copyright Sapienza Università di Roma 2015

Suggested Citation

  • Deepesh Bhati & Mohd. Malik & H. Vaman, 2015. "Lindley–Exponential distribution: properties and applications," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 335-357, December.
    • Handle: RePEc:spr:metron:v:73:y:2015:i:3:p:335-357
    DOI: 10.1007/s40300-015-0060-9
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    References listed on IDEAS

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    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. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    3. Gómez-Déniz, Emilio & Sordo, Miguel A. & Calderín-Ojeda, Enrique, 2014. "The Log–Lindley distribution as an alternative to the beta regression model with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 49-57.
    4. K. Krishnamoorthy & Shubhabrata Mukherjee & Huizhen Guo, 2007. "Inference on Reliability in Two-parameter Exponential Stress–strength Model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(3), pages 261-273, May.
    5. 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.
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    7. 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.
    8. 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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    Cited by:

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