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A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications

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  • M. El-Morshedy
  • M. S. Eliwa
  • H. Nagy

Abstract

This paper introduces a new two-parameter exponentiated discrete Lindley distribution. A wide range of its structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, moments, skewness, kurtosis, stress–strength reliability, mean residual lifetime, mean past lifetime, order statistics and L-moment statistics. The hazard rate function can be increasing, decreasing, decreasing–increasing–decreasing, increasing–decreasing–increasing, unimodal, bathtub, and J-shaped depending on its parameters values. Two methods are used herein to estimate the model parameters, namely, the maximum likelihood, and the proportion. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and proportion estimators. The flexibility of the proposed model is explained by using four distinctive data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive real data in many areas.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:japsta:v:47:y:2020:i:2:p:354-375
    DOI: 10.1080/02664763.2019.1638893
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    Cited by:

    1. Mohamed Aboraya & Haitham M. Yousof & G.G. Hamedani & Mohamed Ibrahim, 2020. "A New Family of Discrete Distributions with Mathematical Properties, Characterizations, Bayesian and Non-Bayesian Estimation Methods," Mathematics, MDPI, vol. 8(10), pages 1-25, September.
    2. Mohamed Ibrahim & M. Masoom Ali & Haitham M. Yousof, 2023. "The Discrete Analogue of the Weibull G Family: Properties, Different Applications, Bayesian and Non-Bayesian Estimation Methods," Annals of Data Science, Springer, vol. 10(4), pages 1069-1106, August.
    3. 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.
    4. Radhakumari Maya & Christophe Chesneau & Anuresha Krishna & Muhammed Rasheed Irshad, 2022. "Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications," Stats, MDPI, vol. 5(3), pages 1-18, August.
    5. Shaul K. Bar-Lev & Ad Ridder, 2022. "The Large Arcsine Exponential Dispersion Model—Properties and Applications to Count Data and Insurance Risk," Mathematics, MDPI, vol. 10(19), pages 1-25, October.
    6. Walid Emam & Yusra Tashkandy & G.G. Hamedani & Mohamed Abdelhamed Shehab & Mohamed Ibrahim & Haitham M. Yousof, 2023. "A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian Inference," Mathematics, MDPI, vol. 11(5), pages 1-28, February.
    7. 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.
    8. Mohamed S. Eliwa & Mahmoud El-Morshedy & Haitham M. Yousof, 2022. "A Discrete Exponential Generalized-G Family of Distributions: Properties with Bayesian and Non-Bayesian Estimators to Model Medical, Engineering and Agriculture Data," Mathematics, MDPI, vol. 10(18), pages 1-29, September.

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