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Properties of some stochastic orders: A unified study

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  • Taizhong Hu
  • Asok K. Nanda
  • Huiliang Xie
  • Zegang Zhu

Abstract

The notions of the likelihood ratio order of degree s (s ≥ 0) are introduced for both continuous and discrete integer‐valued random variables. The new orders for s = 0, 1, and 2 correspond to the likelihood ratio, hazard rate, and mean residual life orders. We obtain some basic properties of the new orders and their up shifted stochastic orders, and derive some closure properties of them. Such a study is meaningful because it throws an important light on the understanding of the properties of the likelihood ratio, hazard rate, and mean residual life orders. On the other hand, the properties of the new orders have potential applications. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:2:p:193-216
    DOI: 10.1002/nav.10111
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    References listed on IDEAS

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    7. 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.
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