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Some results on the proportional reversed hazards model

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  • Crescenzo, Antonio Di

Abstract

The proportional reversed hazards model consists in describing random failure times by a family {[F(x)][theta], [theta]>0} of distribution functions, where F(x) is a baseline distribution function. We show various results on this model related to some topics in reliability theory, including ageing notions of random lifetimes, comparisons based on stochastic orders, and relative ageing of distributions.

Suggested Citation

  • Crescenzo, Antonio Di, 2000. "Some results on the proportional reversed hazards model," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 313-321, December.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:4:p:313-321
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    Citations

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    1. Capaldo, Marco & Di Crescenzo, Antonio & Pellerey, Franco, 2024. "Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems," Statistics & Probability Letters, Elsevier, vol. 206(C).
    2. Li, Xiaohu & Da, Gaofeng, 2010. "Stochastic comparisons in multivariate mixed model of proportional reversed hazard rate with applications," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 1016-1025, April.
    3. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2018. "Optimal hazard models based on partial information," European Journal of Operational Research, Elsevier, vol. 270(2), pages 723-733.
    4. P. Sankaran & V. Gleeja, 2008. "Proportional reversed hazard and frailty models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 333-342, November.
    5. Kundu, Debasis & Gupta, Rameshwar D., 2008. "Generalized exponential distribution: Bayesian estimations," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1873-1883, January.
    6. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    7. Farsam Misagh, 2016. "On Shift-Dependent Cumulative Entropy Measures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-8, June.
    8. Longxiang Fang & Narayanaswamy Balakrishnan & Wenyu Huang & Shuai Zhang, 2023. "Usual stochastic ordering of the sample maxima from dependent distribution‐free random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 99-112, February.
    9. 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.
    10. Emilio Gómez-Déniz & Yuri A. Iriarte & Yolanda M. Gómez & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2021. "Statistical Inference for a General Family of Modified Exponentiated Distributions," Mathematics, MDPI, vol. 9(23), pages 1-18, November.
    11. Laniado Rodas, Henry, 2013. "Allocation policies of redundancies in two-parallel-series and two-series-parallel systems," DES - Working Papers. Statistics and Econometrics. WS ws132622, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Nanda, Asok K. & Bhattacharjee, Subarna & Alam, S.S., 2006. "Properties of proportional mean residual life model," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 880-890, May.
    13. Manuel Franco & Juana-María Vivo & Debasis Kundu, 2020. "A Generator of Bivariate Distributions: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
    14. Modibbo, Umar Muhammad & Arshad, Mohd. & Abdalghani, Omer & Ali, Irfan, 2021. "Optimization and estimation in system reliability allocation problem," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    15. 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.
    16. 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.
    17. 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.
    18. Bartoszewicz, Jaroslaw & Skolimowska, Magdalena, 2006. "Preservation of classes of life distributions and stochastic orders under weighting," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 587-596, March.
    19. Kayid, M. & Izadkhah, S., 2015. "Characterizations of the exponential distribution by the concept of residual life at random time," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 164-169.
    20. Wang, Jiantian & Laniado, Henry, 2015. "A note on allocation policy in two-parallel–series and two-series–parallel systems with respect to likelihood ratio order," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 17-21.
    21. Di Crescenzo, Antonio & Longobardi, Maria, 2004. "A measure of discrimination between past lifetime distributions," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 173-182, April.

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