Stochastic orderings of convolution residuals

In this paper we study convolution residuals , that is, if are independent random variables, we study the distributions, and the properties, of the sums given that , where , and . Various stochastic orders, among convolution residuals based on observations from either one or two samples, are derived...

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Bibliographic Details
Published in:Metrika 2013-05, Vol.76 (4), p.559-576
Main Authors: Amiripour, Fariba, Khaledi, Baha-Eldin, Shaked, Moshe
Format: Article
Language:English
Subjects:
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Summary:In this paper we study convolution residuals , that is, if are independent random variables, we study the distributions, and the properties, of the sums given that , where , and . 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.
ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-012-0404-x