Please enter verification code
Minimax Estimation of the Parameter of ЭРланга Distribution Under Different Loss Functions
Science Journal of Applied Mathematics and Statistics
Volume 4, Issue 5, October 2016, Pages: 229-235
Received: Aug. 31, 2016; Accepted: Sep. 12, 2016; Published: Oct. 8, 2016
Views 3461      Downloads 175
Lanping Li, Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China
Article Tools
Follow on us
The aim of this article is to study the estimation of the parameter of ЭРланга distribution based on complete samples. The Bayes estimators of the parameter of ЭРланга distribution are obtained under three different loss functions, namely, weighted square error loss, squared log error loss and entropy loss functions by using conjugate prior inverse Gamma distribution. Then the minimax estimators of the parameter are derived by using Lehmann’s theorem. Finally, performances of these estimators are compared in terms of risks which obtained under squared error loss function.
Bayes Estimator, Minimax Estimator, Squared Log Error Loss Function, Entropy Loss Function
To cite this article
Lanping Li, Minimax Estimation of the Parameter of ЭРланга Distribution Under Different Loss Functions, Science Journal of Applied Mathematics and Statistics. Vol. 4, No. 5, 2016, pp. 229-235. doi: 10.11648/j.sjams.20160405.16
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.
Lv H. Q., Gao L. H. and Chen C. L., 2002. Э рланга distribution and its application in supportability data analysis. Journal of Academy of Armored Force Engineering, 16 (3): 48-52.
Pan G. T., Wang B. H., Chen C. L., Huang Y. B. and Dang M. T., 2009. The research of interval estimation and hypothetical test of small sample of З рланга distribution. Application of Statistics and Management, 28 (3): 468-472.
Long B., 2013. The estimations of parameter from З рланга distribution under missing data samples. Journal of Jiangxi Normal University (Natural Science), 37 (1): 16-19.
Yu C. M., Chi Y. H., Zhao Z. W., and Song J. F., 2008. Maintenance-decision-oriented modeling and emulating of battlefield injury in campaign macrocosm. Journal of System Simulation, 20 (20): 5669-5671.
Long B., 2015. Bayesian estimation of parameter on Эрлангa distribution under different prior distribution. Mathematics in Practice & Theory, (4): 186-192.
Jiao J., Venkat K., Han Y., Weissman T, 2015. Minimax estimation of functionals of discrete distributions. Information Theory IEEE Transactions on, 61 (5): 2835-2885.
Gao C., Ma Z., Ren Z., Zhou H. H, 2014. Minimax estimation in sparse canonical correlation analysis. Annals of Statistics, 43 (5): 905-912.
Kogan M. M., 2014. LMI-based minimax estimation and filtering under unknown covariances. International Journal of Control, 87 (6): 1216-1226.
Tchrakian T. T., Zhuk S., 2015. A macroscopic traffic data-assimilation framework based on the Fourier–Galerkin method and Minimax estimation [J]. IEEE Transactions on Intelligent Transportation Systems, 16 (1): 452-464.
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.
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.
Dey, S., 2008. Minimax estimation of the parameter of the Rayleigh distribution under quadratic loss function, Data Science Journal, 7 (1): 23-30
Shadrokh, A. and Pazira H., 2010. Minimax estimation on the Minimax distribution, International Journal of Statistics and Systems, 5 (2): 99-118.
Rasheed H. A., Al-Shareefi E. F, 2015. Minimax estimation of the scale parameter of Laplace distribution under squared-log error loss function. Mathematical Theory & Modeling, 5 (1): 183-193.
Li L. P., 2014. Minimax estimation of the parameter of exponential distribution based on record values. International Journal of Information Technology & Computer Science, 6 (6): 47-53.
Li L. P., 2016, Minimax estimation of the parameter of Maxwell distribution under different loss functions, American Journal of Theoretical and Applied Statistics, 5 (4): 202-207.
Li X., Shi Y., Wei J., Chai J., 2007. Empirical Bayes estimators of reliability performances using LINEX loss under progressively Type-II censored samples [J]. Mathematics & Computers in Simulation, 2007, 73 (5): 320-326.
Zellner, A., 1986. Bayesian estimation and prediction using asymmetric loss function. Journal of American statistical Association, 81 (394): 446-451.
Brown L., 1968. Inadmissibility of the usual estimators of scale parameters in problems with unknown location and scale parameters. Annals of Mathematical Statistics, 39 (1): 29-48.
Dey, D. K., Ghosh M. and Srinivasan C., 1987. Simultaneous estimation of parameters under entropy loss, J. Statist. Plan. and Infer., 15 (3): 347-363.
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.
Singh S. K., Singh U. and Kumar D., 2011. Bayesian estimation of the exponentiated Gamma parameter and reliability function under asymmetric loss function. REVSTAT, 9 (3): 247-260.
Nematollahi N., Motamed-Shariati F., 2009. Estimation of the scale parameter of the selected Gamma population under the entropy loss function. Communication in Statistics- Theory and Methods, 38 (7): 208-221.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186