American Journal of Theoretical and Applied Statistics

| Peer-Reviewed |

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

Received: 21 May 2016    Accepted: 06 June 2016    Published: 23 June 2016
Views:       Downloads:

Share This Article

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.

DOI 10.11648/j.ajtas.20160504.16
Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 4, July 2016)
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), 2024. Published by Science Publishing Group

Keywords

Bayes Estimator, Minimax Estimator, Squared Log Error Loss, Entropy Loss, Maxwell Distribution

References
[1] Tyagi R. K. and Bhattacharya S. K., 1989. Bayes estimation of the Maxwell’s velocity distribution function, Statistica, 29 (4): 563-567.
[2] Chaturvedi A. and Rani U., 1998. Classical and Bayesian reliability estimation of the generalized Maxwell failure distribution, Journal of Statistical Research, 32: 113-120.
[3] 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.
[4] 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.
[5] 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.
[6] Krishna H. and Malik M., 2009. Reliability estimation in Maxwell distribution with Type-II censored data. International Journal of Quality & Reliability Management, 26 (2): 184-195.
[7] 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.
[8] Krishna H. and Vivekanand K. K., 2014. Estimation in Maxwell distribution with randomly censored data. Journal of Statistical Computation & Simulation, 85 (17): 1-19.
[9] Rasheed H. A., Khalifa Z. N., 2016. Bayes estimators for the Maxwell distribution under quadratic loss function using different priors. Australian Journal of Basic and Applied Sciences, 10 (6): 97-103.
[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.
[11] Hossain A. M. and Huerta G., 2016. Bayesian Estimation and Prediction for the Maxwell Failure Distribution Based on Type II Censored Data. Open Journal of Statistics, 6 (1): 49-60.
[12] Modi K., Gill V., 2015. Length-biased Weighted Maxwell Distribution. Pakistan Journal of Statistics & Operation Research, 11 (4): 465-472
[13] Wald A., 1950. Statistical Decision Theory, Mc Graw-Hill, New York.
[14] Roy M. K., Podder C. K. and Bhuiyan K. J., 2002. Minimax estimation of the scale parameter of the Weibull distribution for quadratic and MLINEX loss functions, Jahangirnagar University Journal of Science, 25: 277-285.
[15] Podder C. K., Roy M. K., Bhuiyan K. J. and Karim A., 2004. Minimax estimation of the parameter of the Pareto distribution for quadratic and MLINEX loss functions, Pak. J. Statist., 20 (1): 137-149.
[16] Dey S., 2008. Minimax estimation of the parameter of the Rayleigh distribution under quadratic loss function, Data Science Journal, 7: 23-30
[17] Shadrokh A. and Pazira H., 2010. Minimax estimation on the Minimax distribution, International Journal of Statistics and Systems, 5 (2): 99-118.
[18] Zellner A., 1986. Bayesian estimation and prediction using asymmetric loss function. Journal of American statistical Association, 81: 446-451.
[19] Kiapoura A. and Nematollahib N., 2011. Robust Bayesian prediction and estimation under a squared log error loss function. Statistics & Probability Letters, 81 (11): 1717-1724.
[20] Dey D. K., Ghosh M. and Srinivasan C., 1987. Simultaneous estimation of parameters under entropy loss, J. Statist. Plan. and Infer., 15: 347-363.
Author Information
  • Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China

Cite This Article
  • 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://download.sciencepg.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  - 

    Copy | Download

  • Sections