Distribution of the Number of Observations Greater Than the ith Dependent Progressively Type-II Censored Order Statistic and Its Use in Goodness-of-fit Testing |
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| Authors: | M Rezapour M H Alamatsaz N Balakrishnan |
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| Institution: | 1. Department of Statistics, Shahid Bahonar University, Kerman, Iran alamatho@sci.ui.ac.ir;3. Department of Statistics, University of Isfahan, Isfahan, Iran;4. Naghshejahan Institute of Higher Education, Baharestan, Isfahan, Iran;5. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada;6. Department of Statistics, King Abdulaziz University, Jeddah, Saudi Arabia |
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| Abstract: | In a life-testing problem, it may be of interest to investigate the number of observations close to but greater than the median, minimum, or more generally, the ith progressively Type-II censored order statistic (PCOS-II). In this paper, we derive the probability mass and distribution functions of the number of observations greater than the ith PCOS-II for a system with identical components for the cases of independent as well as dependent components. The type of dependence considered among the component lifetimes is through an Archimedean copula. We also provide a goodness-of-fit method for determining the best copula model for a given PCOS-II. Finally, an example is provided to illustrate the results developed here. |
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| Keywords: | Archimedean copula Order statistics Progressive censoring Progressively Type-II censored order statistics Reliability systems Goodness-of-fit test |
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