Volume 5, Issue 6, December 2016, Page: 186-191
Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample
Guobing Fan, Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China
Received: Oct. 5, 2016;       Accepted: Oct. 14, 2016;       Published: Nov. 7, 2016
DOI: 10.11648/j.pamj.20160506.13      View  2483      Downloads  82
Abstract
The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the empirical Bayes estimator also obtained by using maximum likelihood on the basis of Bayes estimator. Finally, the admissibility of a class of inverse linear estimators are discussed under suitable conditions.
Keywords
Admissibility, Bayes and Empirical Bayes Estimators, Progressive Type-II Censored Sample, Entropy Loss Function
To cite this article
Guobing Fan, Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample, Pure and Applied Mathematics Journal. Vol. 5, No. 6, 2016, pp. 186-191. doi: 10.11648/j.pamj.20160506.13
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Cramer E., Navarro J., 2015. Progressive Type-II censoring and coherent systems. Naval Research Logistics, 62(6):512–530.
[2]
Bakoban, R. A., 2015. Parameters estimation of the generalized inverted Rayleigh distribution based on progressive type II censoring. Advances & Applications in Statistics, 47(1): 19-50.
[3]
Ng H. K. T., Chan P. S., Balakrishnan N., 2004. Optimal progressive censoring plans for the Weibull distribution. Technometrics, 46(46):470-481.
[4]
Soliman A. A., Abd-Ellah A. H., Abou-Elheggag N. A., Ahmed E. A., 2012. Modified weibull model: a Bayes study using MCMC approach based on progressive censoring data. Reliability Engineering and System Safety, 100(2): 48-57.
[5]
Yang C., 2000. Statistical analysis of Weibull distributed lifetime data under Type II progressive censoring with binomial removals. Journal of Applied Statistics, 27(8):1033-1043.
[6]
Wu S. J., 2008. Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring[J]. Journal of Applied Statistics, 35(10):1139-1150.
[7]
Cho Y., Sun H., Lee K., 2015. Estimating the entropy of a Weibull distribution under generalized progressive hybrid censoring. Entropy, 17(1):102-122.
[8]
Bhattacharya R., Pradhan B., Dewanji A., 2016. On optimum life-testing plans under Type-II progressive censoring scheme using variable neighborhood search algorithm. Test, 25(2):1-22.
[9]
Laumen B., Cramer E., 2015. Likelihood inference for the lifetime performance index under progressive type-II censoring. Economic Quality Control, 30(2):59-73.
[10]
Khorram E., Farahani Z. S. M., 2016. Statistical inference of weighted exponential lifetimes under progressive type-II censoring scheme. Quality Technology & Quantitative Management, 11(4):433-451.
[11]
Wu S. J., Chang C. T., 2003. Inference in the Pareto distribution based on progressive Type II censoring with random removals. Journal of Applied Statistics, 30(2):163-172.
[12]
Raqab M. Z., Asgharzadeh A., Valiollahi R., 2010. Prediction for Pareto distribution based on progressively Type-II censored samples. Computational Statistics & Data Analysis, 54(54):1732-1743.
[13]
Kulldorff G., Vannman K., 2012. Estimation of the location and scale parameters of a Pareto distribution by linear functions of order statistics. Journal of the American Statistical Association, 68(68):218-227.
[14]
Fu J., Xu A., Tang Y., 2012. Objective Bayesian analysis of Pareto distribution under progressive Type-II censoring. Statistics & Probability Letters, 82(10): 1829-1836.
[15]
Saldaña-Zepeda D. P., Vaquera-Huerta H., Arnold B. C., 2010. A goodness of fit test for the Pareto distribution in the presence of Type II censoring, based on the cumulative hazard function. Computational Statistics & Data Analysis, 54(4): 833-842.
[16]
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.
[17]
Zakerzadeh H., Zahraie S. H. M., 2015. Admissibility in non-regular family under squared-log error loss. Metrika, 78(2): 227-236.
[18]
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.
[19]
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.
[20]
Nancy R. M., 1971. Best linear invariant estimation for Weibull parameters under progressive censoring. Technometrics, 13(3): 521-533.
[21]
Balakrishnan, N. and Aggarwala, R., 2000. Progressive Censoring: Theory, Method and Applications. Boston: Birkhauser Publishers.
[22]
Wang D., Song L., Wang D, et al., 1999. Estimation of the exponential distribution parameter under an entropy loss function based on type II censoring. Chinese Journal of Applied Probability & Statisties, 15(15): 176-186.
[23]
Viveros R., Balakrishnan N., 1994. Interval estimation of parameters of life from progressively censored data. Technometrics, 36(1): 84-91.
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