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Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models

Author

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  • Mansour Shrahili

    (Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Mohamed Kayid

    (Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Mhamed Mesfioui

    (Département de Mathématiques et d’informatique, Université du Québec à Trois-Rivières, 3351, Boulevard des Forges, Trois-Rivières, QC G9A 5H7, Canada)

Abstract

In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained. Numerical simulation studies have also been provided to examine the examples presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4652-:d:1280736
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    References listed on IDEAS

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    2. Jorge Navarro & Yolanda Águila, 2017. "Stochastic comparisons of distorted distributions, coherent systems and mixtures with ordered components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 627-648, November.
    3. S. Kirmani & Ramesh Gupta, 2001. "On the Proportional Odds Model in Survival Analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 203-216, June.
    4. 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.
    5. P. G. Sankaran & M. Dileep Kumar, 2019. "Reliability properties of proportional hazards relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 441-456, May.
    6. Jorge Navarro & Yolanda Águila & Miguel A. Sordo & Alfonso Suárez-Llorens, 2016. "Preservation of Stochastic Orders under the Formation of Generalized Distorted Distributions. Applications to Coherent Systems," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 529-545, June.
    7. Lando, Tommaso & Bertoli-Barsotti, Lucio, 2020. "Distorted stochastic dominance: A generalized family of stochastic orders," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 132-139.
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