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On stochastic comparisons and ageing properties of multivariate proportional hazard rate mixtures

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  • Francisco Germán Badía

    (University of Zaragoza)

  • Hyunju Lee

    (EWHA Womans University)

Abstract

In this paper, we study mixtures of the multivariate proportional hazard model, where the frailty (an unobservable non negative random variable) acts on the hazard rates of lifetimes at the same time to model common risk factors. We investigate ageing properties and dependence between components for the mixture model under study. In addition, we carry out stochastic comparisons assuming dependence between components of the baseline random vector. More specifically, these stochastic comparisons refer to mixture models that share the same frailty random variable but different baseline random vectors. The results are applied for inter epoch times of a non homogeneous mixed Poisson process.

Suggested Citation

  • Francisco Germán Badía & Hyunju Lee, 2020. "On stochastic comparisons and ageing properties of multivariate proportional hazard rate mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 355-375, April.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:3:d:10.1007_s00184-019-00730-9
    DOI: 10.1007/s00184-019-00730-9
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    References listed on IDEAS

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    1. Ebrahim Amini-Seresht & Baha-Eldin Khaledi, 2015. "Multivariate stochastic comparisons of mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 1015-1034, November.
    2. Jorge Navarro & Pedro Hernandez, 2008. "Mean residual life functions of finite mixtures, order statistics and coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 277-298, April.
    3. Belzunce, Félix & Mercader, José-Angel & Ruiz, José-María & Spizzichino, Fabio, 2009. "Stochastic comparisons of multivariate mixture models," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1657-1669, September.
    4. Mulero, Julio & Pellerey, Franco & Rodríguez-Griñolo, Rosario, 2010. "Stochastic comparisons for time transformed exponential models," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 328-333, April.
    5. Neeraj Misra & Sameen Naqvi, 2018. "A unified approach to stochastic comparisons of multivariate mixture models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(19), pages 4724-4740, October.
    6. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
    7. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
    8. J. Jarrahiferiz & M. Kayid & S. Izadkhah, 2019. "Stochastic properties of a weighted frailty model," Statistical Papers, Springer, vol. 60(1), pages 53-72, February.
    9. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    10. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    11. Ji Hwan Cha & Maxim Finkelstein, 2018. "Point Processes for Reliability Analysis," Springer Series in Reliability Engineering, Springer, number 978-3-319-73540-5, February.
    12. Badía, F.G. & Sangüesa, C. & Cha, J.H., 2014. "Stochastic comparison of multivariate conditionally dependent mixtures," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 82-94.
    13. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
    14. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    1. Omid Shojaee & Manoochehr Babanezhad, 2023. "On some stochastic comparisons of arithmetic and geometric mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 499-515, July.
    2. Omid Shojaee & Majid Asadi & Maxim Finkelstein, 2021. "On Some Properties of $$\alpha $$ α -Mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1213-1240, November.

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