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

Lanping Li

doi:doi:10.11648/j.ajtas.20160504.16

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

Lanping Li

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 4)

Received: 21 May 2016 Accepted: 6 June 2016 Published: 23 June 2016

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Abstract

The aim of this article is to study the Bayes estimation and minimax estimation of the parameter of Maxwell distribution. Bayes estimators are obtained with non-informative quasi-prior distribution under different loss functions, namely, weighted squared error loss, squared log error loss and entropy loss functions. Then the minimax estimators of the parameter are obtained by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 4)
DOI	10.11648/j.ajtas.20160504.16
Page(s)	202-207
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, Entropy Loss, Maxwell Distribution

References

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[10]	Gui W., 2014. Double acceptance sampling plan for time truncated life tests based on Maxwell distribution. American Journal of Mathematical & Management Sciences, 33 (2): 98-109.
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APA Style

Lanping Li. (2016). Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions. American Journal of Theoretical and Applied Statistics, 5(4), 202-207. https://doi.org/10.11648/j.ajtas.20160504.16

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ACS Style

Lanping Li. Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions. Am. J. Theor. Appl. Stat. 2016, 5(4), 202-207. doi: 10.11648/j.ajtas.20160504.16

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AMA Style

Lanping Li. Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions. Am J Theor Appl Stat. 2016;5(4):202-207. doi: 10.11648/j.ajtas.20160504.16

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@article{10.11648/j.ajtas.20160504.16,
  author = {Lanping Li},
  title = {Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {4},
  pages = {202-207},
  doi = {10.11648/j.ajtas.20160504.16},
  url = {https://doi.org/10.11648/j.ajtas.20160504.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160504.16},
  abstract = {The aim of this article is to study the Bayes estimation and minimax estimation of the parameter of Maxwell distribution. Bayes estimators are obtained with non-informative quasi-prior distribution under different loss functions, namely, weighted squared error loss, squared log error loss and entropy loss functions. Then the minimax estimators of the parameter are obtained by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks.},
 year = {2016}
}

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TY  - JOUR
T1  - Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions
AU  - Lanping Li
Y1  - 2016/06/23
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160504.16
DO  - 10.11648/j.ajtas.20160504.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 202
EP  - 207
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160504.16
AB  - The aim of this article is to study the Bayes estimation and minimax estimation of the parameter of Maxwell distribution. Bayes estimators are obtained with non-informative quasi-prior distribution under different loss functions, namely, weighted squared error loss, squared log error loss and entropy loss functions. Then the minimax estimators of the parameter are obtained by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks.
VL  - 5
IS  - 4
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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Plain Text BibTeX RIS

APA Style

Lanping Li. (2016). Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions. American Journal of Theoretical and Applied Statistics, 5(4), 202-207. https://doi.org/10.11648/j.ajtas.20160504.16

Copy | Download

ACS Style

Lanping Li. Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions. Am. J. Theor. Appl. Stat. 2016, 5(4), 202-207. doi: 10.11648/j.ajtas.20160504.16

Copy | Download

AMA Style

Lanping Li. Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions. Am J Theor Appl Stat. 2016;5(4):202-207. doi: 10.11648/j.ajtas.20160504.16

Copy | Download

@article{10.11648/j.ajtas.20160504.16,
  author = {Lanping Li},
  title = {Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {4},
  pages = {202-207},
  doi = {10.11648/j.ajtas.20160504.16},
  url = {https://doi.org/10.11648/j.ajtas.20160504.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160504.16},
  abstract = {The aim of this article is to study the Bayes estimation and minimax estimation of the parameter of Maxwell distribution. Bayes estimators are obtained with non-informative quasi-prior distribution under different loss functions, namely, weighted squared error loss, squared log error loss and entropy loss functions. Then the minimax estimators of the parameter are obtained by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions
AU  - Lanping Li
Y1  - 2016/06/23
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160504.16
DO  - 10.11648/j.ajtas.20160504.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 202
EP  - 207
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160504.16
AB  - The aim of this article is to study the Bayes estimation and minimax estimation of the parameter of Maxwell distribution. Bayes estimators are obtained with non-informative quasi-prior distribution under different loss functions, namely, weighted squared error loss, squared log error loss and entropy loss functions. Then the minimax estimators of the parameter are obtained by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks.
VL  - 5
IS  - 4
ER  -

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