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Minimax Estimation of the Parameter of ЭРланга Distribution Under Different Loss Functions

Received: 31 August 2016     Accepted: 12 September 2016     Published: 8 October 2016
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Abstract

The aim of this article is to study the estimation of the parameter of ЭРланга distribution based on complete samples. The Bayes estimators of the parameter of ЭРланга distribution are obtained under three different loss functions, namely, weighted square error loss, squared log error loss and entropy loss functions by using conjugate prior inverse Gamma distribution. Then the minimax estimators of the parameter are derived by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks which obtained under squared error loss function.

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 5)
DOI 10.11648/j.sjams.20160405.16
Page(s) 229-235
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Bayes Estimator, Minimax Estimator, Squared Log Error Loss Function, Entropy Loss Function

References
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  • APA Style

    Lanping Li. (2016). Minimax Estimation of the Parameter of ЭРланга Distribution Under Different Loss Functions. Science Journal of Applied Mathematics and Statistics, 4(5), 229-235. https://doi.org/10.11648/j.sjams.20160405.16

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    ACS Style

    Lanping Li. Minimax Estimation of the Parameter of ЭРланга Distribution Under Different Loss Functions. Sci. J. Appl. Math. Stat. 2016, 4(5), 229-235. doi: 10.11648/j.sjams.20160405.16

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    AMA Style

    Lanping Li. Minimax Estimation of the Parameter of ЭРланга Distribution Under Different Loss Functions. Sci J Appl Math Stat. 2016;4(5):229-235. doi: 10.11648/j.sjams.20160405.16

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  • @article{10.11648/j.sjams.20160405.16,
      author = {Lanping Li},
      title = {Minimax Estimation of the Parameter of ЭРланга Distribution Under Different Loss Functions},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {4},
      number = {5},
      pages = {229-235},
      doi = {10.11648/j.sjams.20160405.16},
      url = {https://doi.org/10.11648/j.sjams.20160405.16},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160405.16},
      abstract = {The aim of this article is to study the estimation of the parameter of ЭРланга distribution based on complete samples. The Bayes estimators of the parameter of ЭРланга distribution are obtained under three different loss functions, namely, weighted square error loss, squared log error loss and entropy loss functions by using conjugate prior inverse Gamma distribution. Then the minimax estimators of the parameter are derived by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks which obtained under squared error loss function.},
     year = {2016}
    }
    

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    T1  - Minimax Estimation of the Parameter of ЭРланга Distribution Under Different Loss Functions
    AU  - Lanping Li
    Y1  - 2016/10/08
    PY  - 2016
    N1  - https://doi.org/10.11648/j.sjams.20160405.16
    DO  - 10.11648/j.sjams.20160405.16
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
    SP  - 229
    EP  - 235
    PB  - Science Publishing Group
    SN  - 2376-9513
    UR  - https://doi.org/10.11648/j.sjams.20160405.16
    AB  - The aim of this article is to study the estimation of the parameter of ЭРланга distribution based on complete samples. The Bayes estimators of the parameter of ЭРланга distribution are obtained under three different loss functions, namely, weighted square error loss, squared log error loss and entropy loss functions by using conjugate prior inverse Gamma distribution. Then the minimax estimators of the parameter are derived by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks which obtained under squared error loss function.
    VL  - 4
    IS  - 5
    ER  - 

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Author Information
  • Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China

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