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Characterizations of the IFR and DFR aging notions by means of the dispersive order

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  • Pellerey, Franco
  • Shaked, Moshe

Abstract

The purpose of this note is to show a new characterization of the IFR and DFR aging notions by means of the dispersive order. Our result extends results of Mailhot (1987) and of Belzunce, Candel and Ruiz (1995). Our method of proof can also be extended to handle comparisons of "past lives", that is, comparisons of [X - tX

Suggested Citation

  • Pellerey, Franco & Shaked, Moshe, 1997. "Characterizations of the IFR and DFR aging notions by means of the dispersive order," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 389-393, May.
    • Handle: RePEc:eee:stapro:v:33:y:1997:i:4:p:389-393
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    Cited by:

    1. Denuit, Michel M. & Mesfioui, Mhamed, 2011. "The dispersive effect of cross-aging with archimedean copulas," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1407-1418, September.
    2. Jongwoo Jeon & Subhash Kochar & Chul Park, 2006. "Dispersive ordering—Some applications and examples," Statistical Papers, Springer, vol. 47(2), pages 227-247, March.
    3. Xia, Wanwan, 2019. "Partial monotonicity of entropy revisited," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 248-253.
    4. José Pablo Arias‐Nicolás & Félix Belzunce & Olga Núñez‐Barrera & Alfonso Suárez‐Llorens, 2009. "A multivariate IFR notion based on the multivariate dispersive ordering," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 339-358, May.
    5. Sordo, M.A. & Bello, A.J. & Suárez-Llorens, A., 2018. "Stochastic orders and co-risk measures under positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 105-113.
    6. Kayid, M. & Alamoudi, L., 2013. "Some results about the exponential ordering of inactivity time," Economic Modelling, Elsevier, vol. 33(C), pages 159-163.
    7. Soo-Haeng Cho & Xin Wang, 2017. "Newsvendor Mergers," Management Science, INFORMS, vol. 63(2), pages 298-316, February.
    8. Belzunce, F., 1999. "On a characterization of right spread order by the increasing convex order," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 103-110, November.
    9. Fernández-Ponce, J.M. & Pellerey, F. & Rodríguez-Griñolo, M.R., 2011. "A characterization of the multivariate excess wealth ordering," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 410-417.
    10. 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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    Keywords

    Aging notions Stochastic orders;

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