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Characterizations of the hazard rate order and IFR aging notion


  • Belzunce, Félix
  • Gao, Xiaoli
  • Hu, Taizhong
  • Pellerey, Franco


The Laplace transform of residual lives order has been recently defined and studied in the literature to compare random lifetimes. Here, we prove that such stochastic order is equivalent to the well-known hazard rate order. As consequences, we get new characterizations of the hazard rate order and increasing in failure rate (IFR) aging notion, in terms also of the mean residual life order and decreasing in mean residual life (DMRL) aging notion.

Suggested Citation

  • Belzunce, Félix & Gao, Xiaoli & Hu, Taizhong & Pellerey, Franco, 2004. "Characterizations of the hazard rate order and IFR aging notion," Statistics & Probability Letters, Elsevier, vol. 70(4), pages 235-242, December.
  • Handle: RePEc:eee:stapro:v:70:y:2004:i:4:p:235-242

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    References listed on IDEAS

    1. Denuit, Michel, 2001. "Laplace transform ordering of actuarial quantities," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 83-102, August.
    2. Thistle, Paul D., 1993. "Negative Moments, Risk Aversion, and Stochastic Dominance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(02), pages 301-311, June.
    3. Belzunce, Félix & Ortega, Eva & Ruiz, José M., 1999. "The Laplace order and ordering of residual lives," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 145-156, April.
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    Cited by:

    1. Kandil Abd El-Fattah Mohamed & Mahdy Mervat Mahdy Ramadan & Kayid Mohamed, 2010. "Median Inactivity Time Function and its Reliability Properties," Stochastics and Quality Control, De Gruyter, vol. 25(2), pages 253-268, January.
    2. Shaked, Moshe & Lillo Rodríguez, Rosa Elvira & Franco Pereira, Alba María, 2010. "The decreasing percentile residual life aging notion," DES - Working Papers. Statistics and Econometrics. WS ws101807, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Belzunce, Felix & Ortega, Eva-Maria & Ruiz, Jose M., 2007. "On non-monotonic ageing properties from the Laplace transform, with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 1-14, January.


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