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Further Properties and Estimations of Exponentiated Generalized Linear Exponential Distribution

Author

Listed:
  • Chien-Tai Lin

    (Department of Mathematics, Tamkang University, New Taipei City 251301, Taiwan)

  • Yu Liu

    (Department of Mathematics, Tamkang University, New Taipei City 251301, Taiwan)

  • Yun-Wei Li

    (Department of Mathematics, Tamkang University, New Taipei City 251301, Taiwan)

  • Zhi-Wei Chen

    (Department of Mathematics, Tamkang University, New Taipei City 251301, Taiwan)

  • Hassan M. Okasha

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Current home address: Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt.)

Abstract

The recent exponentiated generalized linear exponential distribution is a generalization of the generalized linear exponential distribution and the exponentiated generalized linear exponential distribution. In this paper, we study some statistical properties of this distribution such as negative moments, moments of order statistics, mean residual lifetime, and their asymptotic distributions for sample extreme order statistics. Different estimation procedures include the maximum likelihood estimation, the corrected maximum likelihood estimation, the modified maximum likelihood estimation, the maximum product of spacing estimation, and the least squares estimation are compared via a Monte Carlo simulation study in terms of their biases, mean squared errors, and their rates of obtaining reliable estimates. Recommendations are made from the simulation results and a numerical example is presented to illustrate its use for modeling a rainfall data from Orlando, Florida.

Suggested Citation

  • Chien-Tai Lin & Yu Liu & Yun-Wei Li & Zhi-Wei Chen & Hassan M. Okasha, 2021. "Further Properties and Estimations of Exponentiated Generalized Linear Exponential Distribution," Mathematics, MDPI, vol. 9(24), pages 1-31, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3328-:d:707093
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    References listed on IDEAS

    as
    1. Mahmoud, M.A.W. & Alam, Farouq Mohammad A., 2010. "The generalized linear exponential distribution," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1005-1014, June.
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