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Efficient Estimation of the PDF and the CDF of a Generalized Logistic Distribution

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  • Yogesh Mani Tripathi

    (Indian Institute of Technology Patna)

  • Amulya Kumar Mahto

    (Indian Institute of Technology Patna)

  • Sanku Dey

    (St. Anthony’s College)

Abstract

The generalized logistic distribution is a useful extension of the logistic distribution, allowing for increasing and bathtub shaped hazard rates and has been used to model the data with a unimodal density. Here, we consider estimation of the probability density function and the cumulative distribution function of the generalized logistic distribution. The following estimators are considered: maximum likelihood estimator, uniformly minimum variance unbiased estimator (UMVUE), least square estimator, weighted least square estimator, percentile estimator, maximum product spacing estimator, Cramér–von-Mises estimator and Anderson–Darling estimator. Analytical expressions are derived for the bias and the mean squared error. Simulation studies are also carried out to show that the maximum-likelihood estimator is better than the UMVUE and that the UMVUE is better than others. Finally, a real data set has been analyzed for illustrative purposes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aodasc:v:4:y:2017:i:1:d:10.1007_s40745-016-0093-9
    DOI: 10.1007/s40745-016-0093-9
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    References listed on IDEAS

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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. 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.
    4. Klein, Ingo, 2017. "(Generalized) maximum cumulative direct, paired, and residual Φ entropy principle," FAU Discussion Papers in Economics 25/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.

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