An analytic proof of the preservation of the up-shifted likelihood ratio order under convolutions |
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Institution: | Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People''s Republic of China |
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Abstract: | The closure property of the up-shifted likelihood ratio order under convolutions was first proved by Shanthikumar and Yao (Stochastic Process. Appl. 23 (1986) 259) by establishing a stochastic monotonicity property of birth–death processes. Lillo et al. (Recent Advances in Reliability Theory: Methodology, Practice, and Inference. Birkhäuser, Boston, 2000, p. 85) made a slight extension of this closure property for any random variables with interval supports by using the result of Shanthikumar and Yao. A new analytic proof of the closure property is given, and the method is applied to establish another result involving the up-shifted hazard rate and reversed hazard rate orders. |
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