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Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data

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  • Balakrishnan, Narayanaswamy
  • Belzunce, Félix
  • Sordo, Miguel A.
  • Suárez-Llorens, Alfonso

Abstract

In this paper, we establish some results for the increasing convex comparisons of generalized order statistics. First, we prove that if the minimum of two sets of generalized order statistics are ordered in the increasing convex order, then the remaining generalized order statistics are also ordered in the increasing convex order. This result is extended to the increasing directionally convex comparisons of random vectors of generalized order statistics. For establishing this general result, we first prove a new result in that two random vectors with a common conditionally increasing copula are ordered in the increasing directionally convex order if the marginals are ordered in the increasing convex order. This latter result is, of course, of interest in its own right.

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  • Balakrishnan, Narayanaswamy & Belzunce, Félix & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 45-54.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:45-54
    DOI: 10.1016/j.jmva.2011.08.017
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    Cited by:

    1. Mesfioui, Mhamed & Denuit, Michel, 2014. "Comonotonicity, orthant convex order and sums of random variables," LIDAM Discussion Papers ISBA 2014002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Gbari, Samuel & Denuit, Michel, 2014. "Efficient approximations for numbers of survivors in the Lee–Carter model," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 71-77.
    3. Antonia Castaño-Martínez & Gema Pigueiras & Georgios Psarrakos & Miguel A. Sordo, 2020. "Increasing concave orderings of linear combinations of order statistics with applications to social welfare," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 699-712, August.
    4. Chen Li & Xiaohu Li, 2018. "Preservation of increasing convex/concave order under the formation of parallel/series system of dependent components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 445-464, May.
    5. Castaño-Martínez, A. & Pigueiras, G. & Sordo, M.A., 2019. "On a family of risk measures based on largest claims," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 92-97.
    6. Sordo, Miguel A., 2016. "A multivariate extension of the increasing convex order to compare risks," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 224-230.
    7. Mesfioui, Mhamed & Denuit, Michel M., 2015. "Comonotonicity, orthant convex order and sums of random variables," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 356-364.
    8. Maryam Esna-Ashari & Narayanaswamy Balakrishnan & Mahdi Alimohammadi, 2023. "HR and RHR orderings of generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 131-148, January.
    9. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    10. Sordo, Miguel A. & Suárez-Llorens, Alfonso & Bello, Alfonso J., 2015. "Comparison of conditional distributions in portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 62-69.

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