An analytic proof of the preservation of the up-shifted likelihood ratio order under convolutions

Taizhong Hu and Zegang Zhu

Stochastic Processes and their Applications, 2001, vol. 95, issue 1, 55-61

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.

Keywords: Likelihood; ratio; order; Hazard; rate; order; Reversed; hazard; rate; order (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (3)

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