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Mathematical Problems in Engineering
Volume 2016, Article ID 7035279, 12 pages
Research Article

A Mixture of Two Burr Type III Distributions: Identifiability and Estimation under Type II Censoring

Department of Mathematics, College of Science, Aljouf University, P.O. Box 848, Sakaka 42421, Saudi Arabia

Received 16 June 2016; Revised 18 September 2016; Accepted 3 October 2016

Academic Editor: Juan C. Agüero

Copyright © 2016 A. S. Al-Moisheer. This 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.


The mixture of two Burr Type III distributions (MTBIIID) is investigated. First, the identifiability property of the MTBIIID is proved. Then, two different methods of estimation are used. Next, the estimates of the unknown five parameters and reliability function of the MTBIIID under Type II censoring are obtained. To study the performance of the estimation technique in the paper, a Monte Carlo simulation is presented. In addition, the numerical illustration requires solving nonlinear equations; therefore, the software international mathematical statistical library (IMSL) is used to assess these effects numerically. Finally, a real data set is applied to illustrate the methods proposed here.