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On sufficient conditions for mean residual life and related orders

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  • Belzunce, Félix
  • Martínez-Riquelme, Carolina
  • Ruiz, José M.

Abstract

A well known sufficient condition for the mean residual life order of two random variables is the hazard rate order of the two random variables. The hazard rate order is characterized by the monotonicity of the ratio of the two survival functions. However in many cases this ratio is non monotone and the hazard rate order does not hold. The purpose is to show that, in some situations, this non monotonicity is still a sufficient condition for the mean residual life order, under some additional mild conditions. Applications to compare some parametric models of distributions and generalized order statistics are provided. Similar results are given for the mean inactivity time order.

Suggested Citation

  • Belzunce, Félix & Martínez-Riquelme, Carolina & Ruiz, José M., 2013. "On sufficient conditions for mean residual life and related orders," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 199-210.
    • Handle: RePEc:eee:csdana:v:61:y:2013:i:c:p:199-210
    DOI: 10.1016/j.csda.2012.12.005
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    References listed on IDEAS

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    1. Belzunce, F. & Pellerey, Franco & Ruiz, J. M. & Shaked, Moshe, 1997. "The dilation order, the dispersion order, and orderings of residual lives," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 263-275, May.
    2. Hu, Taizhong & Zhuang, Weiwei, 2005. "A note on stochastic comparisons of generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 163-170, April.
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    Cited by:

    1. Antonio Di Crescenzo & Abdolsaeed Toomaj, 2022. "Weighted Mean Inactivity Time Function with Applications," Mathematics, MDPI, vol. 10(16), pages 1-30, August.
    2. Elham Khaleghpanah Noughabi & Majid Chahkandi & Majid Rezaei, 2022. "On the Mean and Variance Residual Life Comparisons of Coherent Systems with Identically Distributed Components," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2801-2822, December.
    3. Jorge Navarro & Franco Pellerey & Miguel A. Sordo, 2020. "Weak Dependence Notions and Their Mutual Relationships," Mathematics, MDPI, vol. 9(1), pages 1-27, December.
    4. Félix Belzunce & Carolina Martínez-Riquelme, 2019. "On the unimodality of the likelihood ratio with applications," Statistical Papers, Springer, vol. 60(1), pages 223-237, February.
    5. Tommaso Lando & Lucio Bertoli-Barsotti, 2020. "Stochastic dominance relations for generalised parametric distributions obtained through composition," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 297-311, December.
    6. Stefanos Leonardos & Costis Melolidakis & Constandina Koki, 2022. "Monopoly pricing in vertical markets with demand uncertainty," Annals of Operations Research, Springer, vol. 315(2), pages 1291-1318, August.
    7. Maryam Esna-Ashari & Narayanaswamy Balakrishnan & Mahdi Alimohammadi, 2023. "HR and RHR orderings of generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 131-148, January.

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