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Power Lindley-G Family of Distributions

Author

Listed:
  • Amal S. Hassan

    (Cairo University)

  • Said G. Nassr

    (Sinai University)

Abstract

In this paper, we introduce a new family of probability distributions generated from a power Lindley random variable called the power Lindley-generated family. The new family extends several classical distributions as well as generalizes the odd Lindley family which is performed by Silva et al. (Austrian J Stat 46:65–87, 2017). Some of the mathematical properties are obtained involving moments, incomplete moments, quantile function and order statistics. New four distributions are provided as special models from the family. The model parameters of the family are estimated by the maximum likelihood technique. An application to real data set and simulation study are provided to demonstrate the flexibility and interest of one special model of the suggested family.

Suggested Citation

  • Amal S. Hassan & Said G. Nassr, 2019. "Power Lindley-G Family of Distributions," Annals of Data Science, Springer, vol. 6(2), pages 189-210, June.
    • Handle: RePEc:spr:aodasc:v:6:y:2019:i:2:d:10.1007_s40745-018-0159-y
    DOI: 10.1007/s40745-018-0159-y
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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. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    3. Ghitany, M.E. & Al-Mutairi, D.K. & Balakrishnan, N. & Al-Enezi, L.J., 2013. "Power Lindley distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 20-33.
    4. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    5. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    6. M. H. Tahir & Gauss M. Cordeiro & Ayman Alzaatreh & M. Mansoor & M. Zubair, 2016. "The logistic-X family of distributions and its applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(24), pages 7326-7349, December.
    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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    2. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
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    5. Mohamed S. Eliwa & Muhammad H. Tahir & Muhammad A. Hussain & Bader Almohaimeed & Afrah Al-Bossly & Mahmoud El-Morshedy, 2023. "Univariate Probability-G Classes for Scattered Samples under Different Forms of Hazard: Continuous and Discrete Version with Their Inferences Tests," Mathematics, MDPI, vol. 11(13), pages 1-24, June.

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