International Scholarly Research Network ISRN Probability and Statistics Volume 2012, Article ID 292384, 15 pages doi:10.5402/2012/292384 Research Article Inference for the Geometric Extreme Exponential Distribution under Progressive Type II Censoring Reza Pakyari Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran Correspondence should be addressed to Reza Pakyari, r-pakyari@araku.ac.ir Received 22 June 2012; Accepted 11 July 2012 Academic Editors: M. Galea and M. Montero Copyright q 2012 Reza Pakyari. 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. Geometric extreme exponential GE-exponential is one of the nonnegative right-skewed distribution that is suitable for analyzing lifetime data. It is well known that the maximum likelihood estimators MLEs of the parameters lead to likelihood equations that have to be solved numerically. In this paper, we provide explicit estimators through an approximation of the likelihood equations based on progressively Type-II-censored samples. The approximate estimators are then used as starting values to find the MLEs numerically. The bias and variances of the MLEs are calculated for a wide range of sample sizes and different progressive censoring schemes through a Monte Carlo simulation study. Moreover, formulas for the observed Fisher information are given which could be used to construct asymptotic confidence intervals. The coverage probabilities of the confidence intervals and the percentage points of pivotal quantities associated with the MLEs are also calculated. A real dataset has been studied for illustrative purposes. 1. Introduction Progressive censoring is one of the important sampling techniques that was first introduced by Herd 1 and its importance in life testing reliability experiments was discussed by Cohen 2. The progressive Type-II censoring is as follows. Suppose n units are placed on test. At the time of the first failure, R 1 units are randomly removed from the n - 1 surviving units. Next, at the time of the second failure, R 2 units are randomly removed from the n - R 1 - 2 surviving units, and so on. Finally, after the mth failure, all remaining R m units are removed. Thus, we observe m complete failures and R 1  R 2  ···  R m items are progressively censored from the n units under test, and so n  m R 1  R 2  ···  R m . The vector R R 1 ,...,R m  is called the censoring scheme and is fixed prior to the study. If R 0,..., 0, no withdrawals are made which correspond to the complete sample and the ordinary order statistics will