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Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Author

Listed:
  • M. S. Eliwa

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Ziyad Ali Alhussain

    (Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia)

  • M. El-Morshedy

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics, College of Sciences and Humanities Studies in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

Abstract

Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions.

Suggested Citation

  • M. S. Eliwa & Ziyad Ali Alhussain & M. El-Morshedy, 2020. "Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications," Mathematics, MDPI, vol. 8(3), pages 1-26, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:358-:d:329553
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    References listed on IDEAS

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    1. Bebbington, Mark & Lai, Chin-Diew & Wellington, Morgan & Zitikis, RiÄ ardas, 2012. "The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 37-44.
    2. Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
    3. M. S. Eliwa & M. El-Morshedy, 2019. "Bivariate Gumbel-G Family of Distributions: Statistical Properties, Bayesian and Non-Bayesian Estimation with Application," Annals of Data Science, Springer, vol. 6(1), pages 39-60, March.
    4. Josmar Mazucheli & André Felipe Menezes & Sanku Dey, 2019. "Unit-Gompertz Distribution with Applications," Statistica, Department of Statistics, University of Bologna, vol. 79(1), pages 25-43.
    5. Morad Alizadeh & Ahmed Z. Afify & M. S. Eliwa & Sajid Ali, 2020. "The odd log-logistic Lindley-G family of distributions: properties, Bayesian and non-Bayesian estimation with applications," Computational Statistics, Springer, vol. 35(1), pages 281-308, March.
    6. M. El-Morshedy & M. S. Eliwa & H. Nagy, 2020. "A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(2), pages 354-375, January.
    7. 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.
    8. Albert C. Bemmaor & Nicolas Glady, 2012. "Modeling Purchasing Behavior with Sudden "Death": A Flexible Customer Lifetime Model," Management Science, INFORMS, vol. 58(5), pages 1012-1021, May.
    9. M. S. Eliwa & M. El-Morshedy & Mohamed Ibrahim, 2019. "Inverse Gompertz Distribution: Properties and Different Estimation Methods with Application to Complete and Censored Data," Annals of Data Science, Springer, vol. 6(2), pages 321-339, June.
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    Cited by:

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    2. Irshad, M.R. & Jodrá, P. & Krishna, A. & Maya, R., 2023. "On the discrete analogue of the Teissier distribution and its associated INAR(1) process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 227-245.
    3. Ehab M. Almetwally & Sanku Dey & Saralees Nadarajah, 2023. "An Overview of Discrete Distributions in Modelling COVID-19 Data Sets," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1403-1430, August.

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