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B0621
Title: Maximum likelihood inference based on censored samples from the geometric distribution Authors:  Anna Dembinska - Warsaw University of Technology, Faculty of Mathematics and Information Science (Poland) [presenting]
Krzysztof Jasinski - Nicolaus Copernicus University (Poland)
Abstract: When high-quality and long-life products are tested, we need special time-effective methods to gain knowledge about their reliability. One method to accelerate life testing is to use Type-II right censoring. During an experiment in which Type-II right censoring is applied, $n$ items with independent and identically distributed lifetimes are placed on a test and the experiment is terminated at the moment of the $r$th failure, where $r<n$ is fixed in advance. Maximum likelihood estimation for the geometric distribution based on Type-II right censored sample is considered. First, general conditions for discrete distributions guaranteeing the almost sure existence of a strongly consistent sequence of maximum likelihood estimators (MLE's) will be given. Then, the discussion will be limited to the case of the geometric distribution, and a closed-form formula for the MLE will be presented. Moreover, some finite-sample properties of the MLE of the geometric parameter will be shown in the special case when $r=1$. In particular, its bias and mean squared error will be obtained. Finally, the results will be generalized to the situation when more than one censored sample is observed.