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On Relative Reversed Hazard Rate Order

Author

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  • Majid Rezaei
  • Behzad Gholizadeh
  • Salman Izadkhah

Abstract

In this paper, through the monotonicity property of reversed hazards ratio, a new stochastic ordering is introduced. Two well-known parametric families of distributions are proved to be ordered with respect to their parameters, according to the new proposed stochastic order. Other situations, where the new order is applicable, are described in details. A number of elementary and basic properties of the order, for example, preservation under increasing transformations are derived. Stochastic comparisons of the parallel systems are made using the new stochastic order. In parallel with the obtained results, some examples will explain the concepts.

Suggested Citation

  • Majid Rezaei & Behzad Gholizadeh & Salman Izadkhah, 2015. "On Relative Reversed Hazard Rate Order," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(2), pages 300-308, January.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:2:p:300-308
    DOI: 10.1080/03610926.2012.745559
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    Citations

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    Cited by:

    1. N. Unnikrishnan Nair & S. M. Sunoj & Rajesh G., 2023. "Relation between Relative Hazard Rates and Residual Divergence with some Applications to Reliability Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 784-802, February.
    2. Mansour Shrahili & Mohamed Kayid & Mhamed Mesfioui, 2023. "Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models," Mathematics, MDPI, vol. 11(22), pages 1-28, November.
    3. M. Kayid & S. Izadkhah & Ming J. Zuo, 2017. "Some results on the relative ordering of two frailty models," Statistical Papers, Springer, vol. 58(2), pages 287-301, June.
    4. Antonio Di Crescenzo & Suchandan Kayal & Abdolsaeed Toomaj, 2019. "A past inaccuracy measure based on the reversed relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 607-631, July.
    5. Fatemeh Hooti & Jafar Ahmadi & N. Balakrishnan, 2022. "Stochastic Comparisons of General Proportional Mean Past Lifetime Frailty Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 844-866, August.
    6. Neeraj Misra & Jisha Francis, 2020. "Relative ageing in frailty and resilience models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(2), pages 171-196, February.
    7. Misra, Neeraj & Francis, Jisha, 2015. "Relative ageing of (n−k+1)-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 272-280.
    8. Mahdy, Mervat, 2016. "Further results related to variance past lifetime class & associated orderings and their properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1148-1160.
    9. Neeraj Misra & Jisha Francis, 2018. "Relative aging of (n − k + 1)‐out‐of‐n systems based on cumulative hazard and cumulative reversed hazard functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 566-575, September.
    10. Weiyong Ding & Rui Fang & Peng Zhao, 2017. "Relative Aging of Coherent Systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 345-354, June.
    11. 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.

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