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Complementary Gamma Zero-Truncated Poisson Distribution and Its Application

Author

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  • Ausaina Niyomdecha

    (Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand)

  • Patchanok Srisuradetchai

    (Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand
    Thammasat University Research Unit in Theoretical and Computational Statistics, Thammasat University, Pathum Thani 12120, Thailand)

Abstract

Numerous lifetime distributions have been developed to assist researchers in various fields. This paper proposes a new continuous three-parameter lifetime distribution called the complementary gamma zero-truncated Poisson distribution (CGZTP), which combines the distribution of the maximum of a series of independently identical gamma-distributed random variables with zero-truncated Poisson random variables. The proposed distribution’s properties, including proofs of the probability density function, cumulative distribution function, survival function, hazard function, and moments, are discussed. The unknown parameters are estimated using the maximum likelihood method, whose asymptotic properties are examined. In addition, Wald confidence intervals are constructed for the CGZTP parameters. Simulation studies are conducted to evaluate the efficacy of parameter estimation, and three real-world data applications demonstrate that CGZTP can be an alternative distribution for fitting data.

Suggested Citation

  • Ausaina Niyomdecha & Patchanok Srisuradetchai, 2023. "Complementary Gamma Zero-Truncated Poisson Distribution and Its Application," Mathematics, MDPI, vol. 11(11), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2584-:d:1164230
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    References listed on IDEAS

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    4. Wenhao Gui & Huainian Zhang & Lei Guo, 2017. "The Complementary Lindley-Geometric Distribution and Its Application in Lifetime Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 316-335, November.
    5. David Hinkley, 1977. "On Quick Choice of Power Transformation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 67-69, March.
    6. Kus, Coskun, 2007. "A new lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4497-4509, May.
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