Admissibility Estimation of Burr Type XI Distribution Under Entropy Loss Function Based on Record Values
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 6, November 2016, Pages: 348-353
Received: Sep. 21, 2016; Accepted: Oct. 1, 2016; Published: Oct. 25, 2016
Views 2675      Downloads 78
Lanping Li, Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China
Article Tools
Follow on us
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.
Admissibility, Bayes and Empirical Bayes Estimators, Record Values, Entropy Loss Function
To cite this article
Lanping Li, Admissibility Estimation of Burr Type XI Distribution Under Entropy Loss Function Based on Record Values, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 6, 2016, pp. 348-353. doi: 10.11648/j.ajtas.20160506.13
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Burr W. I., 1942. Cumulative frequency distribution, Annals of Mathematical Statistics, 13 (217): 215-232.
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.
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.
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.
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.
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.
Feroze, N., Aslam, M., 2012. Bayesian analysis of burr type xi distribution under single and mixture of priors, 2 (11): 487-502.
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.
Chandler K. N., 1952. The distribution and frequency of record values, Journal of the Royal Statistical Society B, 14 (2): 220-228.
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.
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.
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.
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.
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.
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.
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.
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.
Zakerzadeh H., Zahraie S. H. M., 2015. Admissibility in non-regular family under squared-log error loss. Metrika, 78 (2): 227-236.
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.
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.
Kim B. H., Meeden G., 2007. Admissible estimation in an one parameter nonregular family of absolutely continuous distributions. Statistical Papers, 48 (2): 337-345.
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.
Arnold, B. C., Balakrishnan, N., Nagaraja, H. N., 1998. Records. New York: John Wiley & Sons.
Dey D. K., Ghosh M. and Srinivasan C., 1987. Simultaneous estimation of parameters under entropy loss, J. Statist. Plan. and Infer., 15: 347-363.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186