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A sufficient condition of crossing type for the bivariate orthant convex order

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  • Denuit, Michel
  • Mesfioui, Mhamed

Abstract

In this work, we derive a sufficient condition for the orthant convex order based on the single crossing of the respective joint survival functions. This condition is expressed in terms of the generators for Archimedean copulas. Numerical examples show that this condition is valid for members of standard copula families (including the Clayton and Frank ones).

Suggested Citation

  • Denuit, Michel & Mesfioui, Mhamed, 2013. "A sufficient condition of crossing type for the bivariate orthant convex order," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 157-162.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:157-162
    DOI: 10.1016/j.spl.2012.07.014
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    1. Denuit, Michel & Mesfioui, Mhamed, 2010. "Generalized increasing convex and directionally convex orders," LIDAM Reprints ISBA 2010029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Denuit, Michel & Mesfioui, Mhamed, 2010. "Generalized increasing convex and directionally convex orders," LIDAM Discussion Papers ISBA 2010012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

    1. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Discussion Papers ISBA 2019006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. J. M. Fernández-Ponce & M. R. Rodríguez-Griñolo, 2017. "New properties of the orthant convex-type stochastic orders," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 618-637, September.
    3. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 128-139.

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