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Relative Ageing of Population and Subpopulations in Proportional Reversed Hazard Frailty Models

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Emerging Electronics and Automation (E2A 2022)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 1088))

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Abstract

Here, we derive the some set of sufficient conditions of relative stochastic orders in the proportional reversed hazard frailty model represented by random variable X with the random variable \(X|\Theta =\theta \). In particular, we discuss the relative ageing notions using failure rate function, reversed failure rate function, and mean inactivity time function.

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References

  1. Li X, Li Z (2008) A mixture model of proportional reversed hazard rate. Commun Stat Theory Methods 37(18):2953

    Google Scholar 

  2. Gupta RC, Gupta RD (2007) Proportional reversed hazard rate model and its applications. J Sta Plan Inference 137(11):3525

    Google Scholar 

  3. Gupta RC, Gupta RD (2009) General frailty model and stochastic orderings. J Stat Plan Inference 139(9):3277

    Google Scholar 

  4. Li X, Da G (2010) Stochastic comparisons in multivariate mixed model of proportional reversed hazard rate with applications. J Multivariate Anal 101(4):1016

    Google Scholar 

  5. Misra N, Francis J (2020) Relative ageing in frailty and resilience models. Metrika 83(2):171

    Google Scholar 

  6. Kalashnikov VV, Rachev ST (1986) A characterization of queueing models and its stability. In: Prohorov YK et al (eds) Probability theory and mathematical statistics. VNU Science Press, Amsterdam 2:37

    Google Scholar 

  7. Sengupta D, Deshpande JV (1994) Some results on the relative ageing of two life distributions. J Appl Prob 31(4):991

    Google Scholar 

  8. Rezaei M, Gholizadeh B, Izadkhah S (2015) On relative reversed hazard rate order. Commun Stat Theory Methods 44(2):300

    Google Scholar 

  9. Misra N, Francis J, Naqvi S (2017) Some sucient conditions for relative aging of life distributions. Prob Eng Inf Sci 31(1):83

    Google Scholar 

  10. Karlin S (1968) Total positivity, vol 1. Stanford University Press, California

    Google Scholar 

  11. Hazra NK, Nanda AK (2015) A note on warm standby system. Stat Prob Lett 106:30

    Google Scholar 

  12. Khaledi BE (2014) Karlin’s basic composition theorems and stochastic orderings. J Iran Stat Soc 13(2):177

    Google Scholar 

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Acknowledgements

The author acknowledges the financial support from the DST, SERB for the project PDF/2018/004307.

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Correspondence to Jisha Francis .

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Francis, J. (2024). Relative Ageing of Population and Subpopulations in Proportional Reversed Hazard Frailty Models. In: Gabbouj, M., Pandey, S.S., Garg, H.K., Hazra, R. (eds) Emerging Electronics and Automation. E2A 2022. Lecture Notes in Electrical Engineering, vol 1088. Springer, Singapore. https://doi.org/10.1007/978-981-99-6855-8_3

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