Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution

Guobing Fan

doi:doi:10.11648/j.sjams.20160404.12

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Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution

Guobing Fan

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

Received: 21 May 2016 Accepted: 6 June 2016 Published: 29 June 2016

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Abstract

In statistical decision-making, when Bayes estimator is used as the unknown parameter’s estimation, there often exists certain loss. Then the aim of this paper is to study the Bayes estimation for the loss and risk functions of parameter of Maxwell distribution under Rukhin’s loss function. Bayes estimator is derived on the basis of the inverse gamma prior distribution under squared error loss function. Then Bayes estimators of loss and risk function are obtained, respectively. Finally, the conditions of Bayes estimators being conservative are also derived.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 4)
DOI	10.11648/j.sjams.20160404.12
Page(s)	129-133
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, Loss Function, Risk Function, Maxwell Distribution

References

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[2]	Hu G., Li Q., Yu S., 2014. Optimal and minimax prediction in multivariate normal populations under a balanced loss function. Journal of Multivariate Analysis, 128 (14): 154-164.
[3]	Cao L., Tao J., Shi N. Z. and Liu, W., 2015. A stepwise confidence interval procedure under unknown variances based on an asymmetric loss function for toxicological evaluation. Australian & New Zealand Journal of Statistics, 57 (1), 73-98.
[4]	Zakerzadeh H. and Zahraie S. H. M., 2014. Admissibility in non-regular family under squared-log error loss. Metrika, 78 (2): 227-236.
[5]	Ahmed E. A., 2014. Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach. Journal of Applied Statistics, 41 (41): 752-768.
[6]	Xu M. P. and Xiong L. C., 2009. Bayes inference for the loss and risk function in Levy distribution parameter estimation. Mathematics in Practice & Theory, 39 (20): 221-226.
[7]	Xian Z. H., 1993. Bayes inference for loss function. Mathematical Statistics and Applied Probability, 8 (3): 25-30.
[8]	Xia Y. F. and Ma S. L., 2008. Bayes inference of loss and risk function in logarithmic normal distribution parameter estimation. Journal of Lanzhou University of Technology, 34 (1): 131-133.
[9]	Ding X. Y. and Xu M. P., 2014. The Bayes inference for the loss and risk functions of parameters in normal and lognormal distribution. Journal of Jiangxi Normal University (Natural Sciences Edition), 38 (1): 70-73.
[10]	Xu M. P., Ding X. Y. and Yu J., 2013. Bayes inference for the loss and risk functions of Rayleigh distribution parameter estimator. Mathematics in Practice & Theory, 43 (21): 151-156.
[11]	Tyagi, R. K. and Bhattacharya S. K., 1989. Bayes estimation of the Maxwell’s velocity distribution function, Statistica, 29 (4): 563-567.
[12]	Chaturvedi, A. and Rani U., 1998. Classical and Bayesian reliability estimation of the generalized Maxwell failure distribution, Journal of Statistical Research, 32: 113-120.
[13]	Podder C. K. and Roy M. K., 2003. Bayesian estimation of the parameter of Maxwell distribution under MLINEX loss function. Journal of Statistical Studies, 23: 11-16.
[14]	Bekker, A. and Roux J. J., 2005. Reliability characteristics of the Maxwell distribution: a Bayes estimation study, Comm. Stat. Theory & Meth., 34 (11): 2169-2178.
[15]	Dey S. and Sudhansu S. M., 2010. Bayesian estimation of the parameter of Maxwell distribution under different loss functions. Journal of Statistical Theory & Practice, 4 (2): 279-287.
[16]	Krishna H. and Malik M., 2011. Reliability estimation in Maxwell distribution with progressively Type-II censored data. Journal of Statistical Computation & Simulation, 82 (4): 1-19.

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APA Style

Guobing Fan. (2016). Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution. Science Journal of Applied Mathematics and Statistics, 4(4), 129-133. https://doi.org/10.11648/j.sjams.20160404.12

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ACS Style

Guobing Fan. Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution. Sci. J. Appl. Math. Stat. 2016, 4(4), 129-133. doi: 10.11648/j.sjams.20160404.12

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AMA Style

Guobing Fan. Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution. Sci J Appl Math Stat. 2016;4(4):129-133. doi: 10.11648/j.sjams.20160404.12

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@article{10.11648/j.sjams.20160404.12,
  author = {Guobing Fan},
  title = {Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {4},
  number = {4},
  pages = {129-133},
  doi = {10.11648/j.sjams.20160404.12},
  url = {https://doi.org/10.11648/j.sjams.20160404.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160404.12},
  abstract = {In statistical decision-making, when Bayes estimator is used as the unknown parameter’s estimation, there often exists certain loss. Then the aim of this paper is to study the Bayes estimation for the loss and risk functions of parameter of Maxwell distribution under Rukhin’s loss function. Bayes estimator is derived on the basis of the inverse gamma prior distribution under squared error loss function. Then Bayes estimators of loss and risk function are obtained, respectively. Finally, the conditions of Bayes estimators being conservative are also derived.},
 year = {2016}
}

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TY  - JOUR
T1  - Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution
AU  - Guobing Fan
Y1  - 2016/06/29
PY  - 2016
N1  - https://doi.org/10.11648/j.sjams.20160404.12
DO  - 10.11648/j.sjams.20160404.12
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  - 129
EP  - 133
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20160404.12
AB  - In statistical decision-making, when Bayes estimator is used as the unknown parameter’s estimation, there often exists certain loss. Then the aim of this paper is to study the Bayes estimation for the loss and risk functions of parameter of Maxwell distribution under Rukhin’s loss function. Bayes estimator is derived on the basis of the inverse gamma prior distribution under squared error loss function. Then Bayes estimators of loss and risk function are obtained, respectively. Finally, the conditions of Bayes estimators being conservative are also derived.
VL  - 4
IS  - 4
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). Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution. Science Journal of Applied Mathematics and Statistics, 4(4), 129-133. https://doi.org/10.11648/j.sjams.20160404.12

Copy | Download

ACS Style

Guobing Fan. Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution. Sci. J. Appl. Math. Stat. 2016, 4(4), 129-133. doi: 10.11648/j.sjams.20160404.12

Copy | Download

AMA Style

Guobing Fan. Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution. Sci J Appl Math Stat. 2016;4(4):129-133. doi: 10.11648/j.sjams.20160404.12

Copy | Download

@article{10.11648/j.sjams.20160404.12,
  author = {Guobing Fan},
  title = {Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {4},
  number = {4},
  pages = {129-133},
  doi = {10.11648/j.sjams.20160404.12},
  url = {https://doi.org/10.11648/j.sjams.20160404.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160404.12},
  abstract = {In statistical decision-making, when Bayes estimator is used as the unknown parameter’s estimation, there often exists certain loss. Then the aim of this paper is to study the Bayes estimation for the loss and risk functions of parameter of Maxwell distribution under Rukhin’s loss function. Bayes estimator is derived on the basis of the inverse gamma prior distribution under squared error loss function. Then Bayes estimators of loss and risk function are obtained, respectively. Finally, the conditions of Bayes estimators being conservative are also derived.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution
AU  - Guobing Fan
Y1  - 2016/06/29
PY  - 2016
N1  - https://doi.org/10.11648/j.sjams.20160404.12
DO  - 10.11648/j.sjams.20160404.12
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  - 129
EP  - 133
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20160404.12
AB  - In statistical decision-making, when Bayes estimator is used as the unknown parameter’s estimation, there often exists certain loss. Then the aim of this paper is to study the Bayes estimation for the loss and risk functions of parameter of Maxwell distribution under Rukhin’s loss function. Bayes estimator is derived on the basis of the inverse gamma prior distribution under squared error loss function. Then Bayes estimators of loss and risk function are obtained, respectively. Finally, the conditions of Bayes estimators being conservative are also derived.
VL  - 4
IS  - 4
ER  -

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