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Transmuted Shifted Lindley Distribution: Characterizations, Classical and Bayesian Estimation with Applications

Author

Listed:
  • A. Chakraborty

    (Visva-Bharati)

  • S. Rana

    (Visva-Bharati)

  • S. I. Maiti

    (Visva-Bharati)

Abstract

In this article, we propose the quadratic rank transmutation map approach on shifted Lindley distribution to improve the existing distribution further. An additional skewness parameter $$\lambda $$ λ is incorporated to transmute the distribution. The distribution, hence introduced, is called the Transmuted Shifted Lindley distribution. We provide a comprehensive description of this distribution’s statistical properties and its reliability behavior. The heat maps on the associated parameters are presented. In the estimation section, both maximum likelihood and Bayesian estimation of parameters are discussed. A detailed simulation study is performed. Finally, a real data application illustrates the performance of fitting to the proposed distribution.

Suggested Citation

  • A. Chakraborty & S. Rana & S. I. Maiti, 2025. "Transmuted Shifted Lindley Distribution: Characterizations, Classical and Bayesian Estimation with Applications," Annals of Data Science, Springer, vol. 12(4), pages 1237-1264, August.
    • Handle: RePEc:spr:aodasc:v:12:y:2025:i:4:d:10.1007_s40745-024-00562-z
    DOI: 10.1007/s40745-024-00562-z
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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. Majdah M. Badr & Ibrahim Elbatal & Farrukh Jamal & Christophe Chesneau & Mohammed Elgarhy, 2020. "The Transmuted Odd Fréchet-G Family of Distributions: Theory and Applications," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    3. Daniele Cristina Tita Granzotto & Francisco Louzada, 2015. "The Transmuted Log-Logistic Distribution: Modeling, Inference, and an Application to a Polled Tabapua Race Time up to First Calving Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(16), pages 3387-3402, August.
    4. 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.
    5. 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.
    6. James M. Tien, 2017. "Internet of Things, Real-Time Decision Making, and Artificial Intelligence," Annals of Data Science, Springer, vol. 4(2), pages 149-178, June.
    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.
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