Pure and Applied Mathematics Journal

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Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample

Received: 05 October 2016    Accepted: 14 October 2016    Published: 07 November 2016
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Abstract

The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the empirical Bayes estimator also obtained by using maximum likelihood on the basis of Bayes estimator. Finally, the admissibility of a class of inverse linear estimators are discussed under suitable conditions.

DOI 10.11648/j.pamj.20160506.13
Published in Pure and Applied Mathematics Journal (Volume 5, Issue 6, December 2016)
Page(s) 186-191
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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), 2024. Published by Science Publishing Group

Keywords

Admissibility, Bayes and Empirical Bayes Estimators, Progressive Type-II Censored Sample, Entropy Loss Function

References
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[16] Wen D. L., Levy M. S., 2006. Admissibility of Bayes estimates under BLINEX loss for the normal mean problem. Communications in Statistics-Theory and Methods, 30(1): 155-163.
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Author Information
  • Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China

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  • APA Style

    Guobing Fan. (2016). Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample. Pure and Applied Mathematics Journal, 5(6), 186-191. https://doi.org/10.11648/j.pamj.20160506.13

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    ACS Style

    Guobing Fan. Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample. Pure Appl. Math. J. 2016, 5(6), 186-191. doi: 10.11648/j.pamj.20160506.13

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    AMA Style

    Guobing Fan. Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample. Pure Appl Math J. 2016;5(6):186-191. doi: 10.11648/j.pamj.20160506.13

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  • @article{10.11648/j.pamj.20160506.13,
      author = {Guobing Fan},
      title = {Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample},
      journal = {Pure and Applied Mathematics Journal},
      volume = {5},
      number = {6},
      pages = {186-191},
      doi = {10.11648/j.pamj.20160506.13},
      url = {https://doi.org/10.11648/j.pamj.20160506.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20160506.13},
      abstract = {The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the empirical Bayes estimator also obtained by using maximum likelihood on the basis of Bayes estimator. Finally, the admissibility of a class of inverse linear estimators are discussed under suitable conditions.},
     year = {2016}
    }
    

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    AB  - The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the empirical Bayes estimator also obtained by using maximum likelihood on the basis of Bayes estimator. Finally, the admissibility of a class of inverse linear estimators are discussed under suitable conditions.
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