American Journal of Theoretical and Applied Statistics

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Admissibility Estimation of Burr Type XI Distribution Under Entropy Loss Function Based on Record Values

Received: 21 September 2016    Accepted: 01 October 2016    Published: 25 October 2016
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Abstract

The aim of this paper is to study the estimation of parameter of Burr Type XI distribution on the basis of lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes and empirical Bayes estimators of the unknown parameter are derived under entropy loss function. Finally, the admissibility and inadmissibility of a class of inverse linear estimators are discussed.

DOI 10.11648/j.ajtas.20160506.13
Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 6, November 2016)
Page(s) 348-353
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

Admissibility, Bayes and Empirical Bayes Estimators, Record Values, Entropy Loss Function

References
[1] Burr W. I., 1942. Cumulative frequency distribution, Annals of Mathematical Statistics, 13 (217): 215-232.
[2] Abdel-Hamid A. H., 2009. Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring, Computational Statistics & Data Analysis, 53 (7): 2511-2523.
[3] Panahi H., Sayyareh A., 2014. Parameter estimation and prediction of order statistics for the Burr Type XII distribution with Type II censoring, Journal of Applied Statistics, 41 (1): 215-232.
[4] Tsai T. R., Lio Y., Jiang N., Fan Y. Y., 2015. Economical sampling plans with warranty based on truncated data from Burr type XII distribution, Journal of the Operational Research Society, 66 (9): 1511-1518.
[5] Wu J. W., Yu H. Y., 2005. Statistical inference about the shape parameter of the Burr type XII distribution under the failure-censored sampling plan, International Journal of Information & Management Sciences, 163 (1): 443-482.
[6] Belaghi R. A., Arashi M., Tabatabaey S. M. M., 2014. Improved confidence intervals for the scale parameter of Burr XII model based on record values, Computational Statistics, 29 (5): 1153-1173.
[7] Feroze, N., Aslam, M., 2012. Bayesian analysis of burr type xi distribution under single and mixture of priors, 2 (11): 487-502.
[8] Feroze N., Aslam M., Saleem A., 2014. Bayesian estimation and prediction of Burr type XI distribution under singly and doubly censored samples, International Journal of Hybrid Information Technology, 7 (2): 331-346.
[9] Chandler K. N., 1952. The distribution and frequency of record values, Journal of the Royal Statistical Society B, 14 (2): 220-228.
[10] Amin E. A., 2012. Bayesian and non-Bayesian estimation from type I generalized logistic distribution based on lower record values, Journal of Applied Sciences Research, 2012 (1): 118-126.
[11] Selim M. A., 2012. Bayesian estimations from the two-parameter bathtub-shaped lifetime distribution based on record values, Pakistan Journal of Statistics & Operation Research, 8 (2): 155-165.
[12] Zakerzadeh H., Jafari A. A., 2015, Inference on the parameters of two Weibull distributions based on record values, Statistical Methods & Applications, 24 (1): 25-40.
[13] El-Sayed M. A., Abd-Elmougod G. A., Abdel-Khalek S., Abd-Elmougod G. A., Abdel-Khalek S., 2013. Bayesian and non-Bayesian estimation of topp-leone distribution based lower record values, 45 (2): 133-145.
[14] Wang B. X., Ye Z. S., Wang B. X., Ye Z. S., 2015. Inference on the Weibull distribution based on record values. Computational Statistics & Data Analysis, 83: 26-36.
[15] Arabi Belaghi, R., Arashi M., Tabatabaey S., 2014. Improved confidence intervals for the scale parameter of Burr XII model based on record values. Computational Statistics, 29 (5): 1153-1173.
[16] Barranco-Chamorro I., Moreno-Rebollo J. L., Jiménez-Gamero M. D., Alba-Fernández M. V., 2015. Estimation of the sample size based on record values. Mathematics & Computers in Simulation, 55 (118): 58-72.
[17] Wen D. L., Levy M. S., 2006. Admissibility of bayes estimates under BLINEX loss for the normal mean problem. Communications in Statistics-Theory and Methods, 30 (1): 155-163.
[18] Zakerzadeh H., Zahraie S. H. M., 2015. Admissibility in non-regular family under squared-log error loss. Metrika, 78 (2): 227-236.
[19] Cao, M. X., & Kong, F. C. (2013). General admissibility for linear estimators in a general multivariate linear model under balanced loss function. Acta Mathematica Sinica, 29 (29): 1823-1832.
[20] Hara, H., Takemura, A., 2009. Bayes admissible estimation of the means in poisson decomposable graphical models. Journal of Statistical Planning & Inference, 139 (4): 1297-1319.
[21] Kim B. H., Meeden G., 2007. Admissible estimation in an one parameter nonregular family of absolutely continuous distributions. Statistical Papers, 48 (2): 337-345.
[22] Mahmoudi E., 2012. Admissible and minimax estimators of θ with truncated parameter space under squared-log error loss function. Communication in Statistics-Theory and Methods, 41 (7): 1242-1253.
[23] Arnold, B. C., Balakrishnan, N., Nagaraja, H. N., 1998. Records. New York: John Wiley & Sons.
[24] 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

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  • APA Style

    Lanping Li. (2016). Admissibility Estimation of Burr Type XI Distribution Under Entropy Loss Function Based on Record Values. American Journal of Theoretical and Applied Statistics, 5(6), 348-353. https://doi.org/10.11648/j.ajtas.20160506.13

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    ACS Style

    Lanping Li. Admissibility Estimation of Burr Type XI Distribution Under Entropy Loss Function Based on Record Values. Am. J. Theor. Appl. Stat. 2016, 5(6), 348-353. doi: 10.11648/j.ajtas.20160506.13

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    AMA Style

    Lanping Li. Admissibility Estimation of Burr Type XI Distribution Under Entropy Loss Function Based on Record Values. Am J Theor Appl Stat. 2016;5(6):348-353. doi: 10.11648/j.ajtas.20160506.13

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  • @article{10.11648/j.ajtas.20160506.13,
      author = {Lanping Li},
      title = {Admissibility Estimation of Burr Type XI Distribution Under Entropy Loss Function Based on Record Values},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {5},
      number = {6},
      pages = {348-353},
      doi = {10.11648/j.ajtas.20160506.13},
      url = {https://doi.org/10.11648/j.ajtas.20160506.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20160506.13},
      abstract = {The aim of this paper is to study the estimation of parameter of Burr Type XI distribution on the basis of lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes and empirical Bayes estimators of the unknown parameter are derived under entropy loss function. Finally, the admissibility and inadmissibility of a class of inverse linear estimators are discussed.},
     year = {2016}
    }
    

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    JO  - American Journal of Theoretical and Applied Statistics
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    AB  - The aim of this paper is to study the estimation of parameter of Burr Type XI distribution on the basis of lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes and empirical Bayes estimators of the unknown parameter are derived under entropy loss function. Finally, the admissibility and inadmissibility of a class of inverse linear estimators are discussed.
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