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Two Families of Continuous Probability Distributions Generated by the Discrete Lindley Distribution

Author

Listed:
  • Srdjan Kadić

    (Faculty of Science and Mathematics, University of Montenegro, 81000 Podgorica, Montenegro
    These authors contributed equally to this work.)

  • Božidar V. Popović

    (Faculty of Science and Mathematics, University of Montenegro, 81000 Podgorica, Montenegro
    These authors contributed equally to this work.)

  • Ali İ. Genç

    (Department of Statistics, Cukurova University, 01290 Adana, Turkey
    These authors contributed equally to this work.)

Abstract

In this paper, we construct two new families of distributions generated by the discrete Lindley distribution. Some mathematical properties of the new families are derived. Some special distributions from these families can be constructed by choosing some baseline distributions, such as exponential, Pareto and standard logistic distributions. We study in detail the properties of the two models resulting from the exponential baseline, among others. These two models have different shape characteristics. The model parameters are estimated by maximum likelihood, and related algorithms are proposed for the computation of the estimates. The existence of the maximum-likelihood estimators is discussed. Two applications prove its usefulness in real data fitting.

Suggested Citation

  • Srdjan Kadić & Božidar V. Popović & Ali İ. Genç, 2023. "Two Families of Continuous Probability Distributions Generated by the Discrete Lindley Distribution," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:290-:d:1026772
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    References listed on IDEAS

    as
    1. Saralees Nadarajah & Božidar Popović & Miroslav Ristić, 2013. "Compounding: an R package for computing continuous distributions obtained by compounding a continuous and a discrete distribution," Computational Statistics, Springer, vol. 28(3), pages 977-992, June.
    2. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.
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