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

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  • Hu, Taizhong
  • Zhu, Zegang

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.

Suggested Citation

  • Hu, Taizhong & Zhu, Zegang, 2001. "An analytic proof of the preservation of the up-shifted likelihood ratio order under convolutions," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 55-61, September.
    • Handle: RePEc:eee:spapps:v:95:y:2001:i:1:p:55-61
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    References listed on IDEAS

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    1. Shanthikumar, J. George & Yao, David D., 1986. "The preservation of likelihood ratio ordering under convolution," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 259-267, December.
    2. Belzunce, Félix & Ruiz, José M. & Shaked, Moshe, 2000. "Stochastic comparisons of nonhomogeneous processes," DES - Working Papers. Statistics and Econometrics. WS 9866, Universidad Carlos III de Madrid. Departamento de Estadística.
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    Cited by:

    1. Belzunce, Félix & Ruiz, José M. & Ruiz, M. Carmen, 2002. "On preservation of some shifted and proportional orders by systems," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 141-154, November.
    2. Taizhong Hu & Asok K. Nanda & Huiliang Xie & Zegang Zhu, 2004. "Properties of some stochastic orders: A unified study," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(2), pages 193-216, March.
    3. Denuit, Michel & Robert, Christian Y., 2023. "Conditional mean risk sharing of independent discrete losses in large pools," LIDAM Discussion Papers ISBA 2023010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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