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Shrinkage Estimation for Location and Scale Parameters of Logistic Distribution Under Record Values

Author

Listed:
  • Shubham Gupta

    (Indian Institute of Technology)

  • Gajendra K. Vishwakarma

    (Indian Institute of Technology)

  • A. M. Elsawah

    (Department of Statistics and Data Science, Faculty of Science and Technology, Beijing Normal University-Hong Kong Baptist University United International College
    BNU-HKBU United International College
    Zagazig University)

Abstract

Logistic distribution (LogDis) is frequently used in many different applications, such as logistic regression, logit models, classification, neural networks, physical sciences, sports modeling, finance and health and disease studies. For instance, the distribution function of the LogDis has the same functional form as the derivative of the Fermi function that can be used to set the relative weight of various electron energies in their contributions to electron transport. The LogDis has wider tails than a normal distribution (NorDis), so it is more consistent with the underlying data and provides better insight into the likelihood of extreme events. For this reason the United States Chess Federation has switched its formula for calculating chess ratings from the NorDis to the LogDis. The outcomes of many real-life experiments are sequences of record-breaking data sets, where only observations that exceed (or only those that fall below) the current extreme value are recorded. The practice demonstrated that the widely used estimators of the scale and location parameters of logistic record values, such as the best linear unbiased estimators (BLUEs), have some defects. This paper investigates the shrinkage estimators of the location and scale parameters for logistic record values using prior information about their BLUEs. Theoretical and computational justifications for the accuracy and precision of the proposed shrinkage estimators are investigated via their bias and mean square error (MSE), which provide sufficient conditions for improving the proposed shrinkage estimators to get unbiased estimators with minimum MSE. The performance of the proposed shrinkage estimators is compared with the performances of the BLUEs. The results demonstrate that the resulting shrinkage estimators are shown to be remarkably efficient.

Suggested Citation

  • Shubham Gupta & Gajendra K. Vishwakarma & A. M. Elsawah, 2024. "Shrinkage Estimation for Location and Scale Parameters of Logistic Distribution Under Record Values," Annals of Data Science, Springer, vol. 11(4), pages 1209-1224, August.
    • Handle: RePEc:spr:aodasc:v:11:y:2024:i:4:d:10.1007_s40745-023-00492-2
    DOI: 10.1007/s40745-023-00492-2
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    References listed on IDEAS

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    1. Tatsuya Kubokawa & William E. Strawderman & Ryota Yuasa, 2020. "Shrinkage estimation of location parameters in a multivariate skew-normal distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(8), pages 2008-2024, April.
    2. F. R. Oliver, 1964. "Methods of Estimating the Logistic Growth Function," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 13(2), pages 57-66, June.
    3. M. A. Alawady & A. M. Elsawah & Jianwei Hu & Hong Qin, 2017. "Asymptotic random extremal ratio and product based on generalized order statistics and its dual," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 8881-8896, September.
    4. Qazi J. Azhad & Mohd. Arshad & Amit Kumar Misra, 2021. "Estimation of common location parameter of several heterogeneous exponential populations based on generalized order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(10), pages 1798-1815, July.
    5. Balakrishnan, N. & Chan, P. S., 1998. "On the normal record values and associated inference," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 73-80, July.
    6. Housila Singh & Sushil Shukla, 2003. "A family of shrinkage estimators for the square of mean in normal distribution," Statistical Papers, Springer, vol. 44(3), pages 433-442, July.
    7. H. M. Barakat & E. M. Nigm & A. M. Elsawah, 2015. "Asymptotic Distributions of the Generalized Range, Midrange, Extremal Quotient, and Extremal Product, with a Comparison Study," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(5), pages 900-913, March.
    8. Marchand, Éric & Strawderman, William E., 2020. "On shrinkage estimation for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    9. 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.
    10. Marco Burkschat & Erhard Cramer & Udo Kamps, 2003. "Dual generalized order statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 13-26.
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