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

Lanping Li

doi:doi:10.11648/j.sjams.20160405.16

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

Lanping Li

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 5)

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

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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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TY  - JOUR
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

Lanping Li

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

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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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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  -

Copy | Download