Stochastic orderings of convolution residuals |
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Authors: | Fariba Amiripour Baha-Eldin Khaledi Moshe Shaked |
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Institution: | 1. Department of Statistics, Razi University, Kermanshah, Iran 3. Islamic Azad University, Kermanshah Branch, Kermanshah, Iran 2. Department of Mathematics, University of Arizona, Tucson, AZ, USA
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Abstract: | In this paper we study convolution residuals, that is, if $X_1,X_2,\ldots ,X_n$ are independent random variables, we study the distributions, and the properties, of the sums $\sum _{i=1}^lX_i-t$ given that $\sum _{i=1}^kX_i>t$ , where $t\in \mathbb R $ , and $1\le k\le l\le n$ . Various stochastic orders, among convolution residuals based on observations from either one or two samples, are derived. As a consequence computable bounds on the survival functions and on the expected values of convolution residuals are obtained. Some applications in reliability theory and queueing theory are described. |
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