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

Guobing Fan

doi:doi:10.11648/j.pamj.20160506.13

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

Guobing Fan

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 6)

Received: 5 October 2016 Accepted: 14 October 2016 Published: 7 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.

Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 6)
DOI	10.11648/j.pamj.20160506.13
Page(s)	186-191
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

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

References

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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample
AU  - Guobing Fan
Y1  - 2016/11/07
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160506.13
DO  - 10.11648/j.pamj.20160506.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 186
EP  - 191
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160506.13
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.
VL  - 5
IS  - 6
ER  -

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Author Information

Guobing Fan

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

Copy | Download

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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample
AU  - Guobing Fan
Y1  - 2016/11/07
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160506.13
DO  - 10.11648/j.pamj.20160506.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 186
EP  - 191
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160506.13
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.
VL  - 5
IS  - 6
ER  -

Copy | Download