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Evaluation and Comparison of Estimators in the Gompertz Distribution

Author

Listed:
  • Sanku Dey

    (St. Anthony’s College)

  • Tanmay Kayal

    (Indian Institute of Technology Patna)

  • Yogesh Mani Tripathi

    (Indian Institute of Technology Patna)

Abstract

This article addresses the different methods of estimation of the probability density function and the cumulative distribution function for the Gompertz distribution. Following estimation methods are considered: maximum likelihood estimators, uniformly minimum variance unbiased estimators, least squares estimators, weighted least square estimators, percentile estimators, maximum product of spacings estimators, Cramér–von-Mises estimators, Anderson–Darling estimators. Monte Carlo simulations are performed to compare the behavior of the proposed methods of estimation for different sample sizes. Finally, one real data set and one simulated data set are analyzed for illustrative purposes.

Suggested Citation

  • Sanku Dey & Tanmay Kayal & Yogesh Mani Tripathi, 2018. "Evaluation and Comparison of Estimators in the Gompertz Distribution," Annals of Data Science, Springer, vol. 5(2), pages 235-258, June.
    • Handle: RePEc:spr:aodasc:v:5:y:2018:i:2:d:10.1007_s40745-017-0126-z
    DOI: 10.1007/s40745-017-0126-z
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    References listed on IDEAS

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    1. Durot, Cécile & Huet, Sylvie & Koladjo, François & Robin, Stéphane, 2013. "Least-squares estimation of a convex discrete distribution," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 282-298.
    2. Yogesh Mani Tripathi & Tanmay Kayal & Sanku Dey, 2017. "Estimation of the PDF and the CDF of exponentiated moment exponential distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1282-1296, November.
    3. Kundu, Debasis & Raqab, Mohammad Z., 2005. "Generalized Rayleigh distribution: different methods of estimations," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 187-200, April.
    4. Badiollah Asrabadi, 1990. "Estimation in the pareto distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 37(1), pages 199-205, December.
    5. Yogesh Mani Tripathi & Amulya Kumar Mahto & Sanku Dey, 2017. "Efficient Estimation of the PDF and the CDF of a Generalized Logistic Distribution," Annals of Data Science, Springer, vol. 4(1), pages 63-81, March.
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    Cited by:

    1. Amal S. Hassan & Salwa M. Assar & Kareem A. Ali & Heba F. Nagy, 2021. "Estimation of the density and cumulative distribution functions of the exponentiated Burr XII distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 171-189, December.
    2. Hassan Amal S. & Assar Salwa M. & Ali Kareem A. & Nagy Heba F., 2021. "Estimation of the density and cumulative distribution functions of the exponentiated Burr XII distribution," Statistics in Transition New Series, Statistics Poland, vol. 22(4), pages 171-189, December.
    3. Shama, M.S. & Dey, Sanku & Altun, Emrah & Afify, Ahmed Z., 2022. "The Gamma–Gompertz distribution: Theory and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 689-712.

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