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Partially Schur-constant models

Author

Listed:
  • Anna Castañer

    (UB - Universitat de Barcelona)

  • M. Mercè Claramunt
  • Claude Lefèvre

    (ULB - Université libre de Bruxelles)

  • Stéphane Loisel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

In this paper, we introduce a new multivariate dependence model that generalizes the standard Schur-constant model. The difference is that the random vector considered is partially exchangeable, instead of exchangeable, whence the term partially Schur-constant. Its advantage is to allow some heterogeneity of marginal distributions and a more flexible dependence structure, which broadens the scope of potential applications. We first show that the associated joint survival function is a monotonic multivariate function. Next, we derive two distributional representations that provide an intuitive understanding of the underlying dependence. Several other properties are obtained, including correlations within and between subvectors. As an illustration, we explain how such a model could be applied to risk management for insurance networks.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Anna Castañer & M. Mercè Claramunt & Claude Lefèvre & Stéphane Loisel, 2019. "Partially Schur-constant models," Post-Print hal-01998057, HAL.
    • Handle: RePEc:hal:journl:hal-01998057
    Note: View the original document on HAL open archive server: https://hal.science/hal-01998057v1
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    References listed on IDEAS

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    1. Shenkman, Natalia, 2017. "A natural parametrization of multivariate distributions with limited memory," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 234-251.
    2. Claude Lefèvre & Stéphane Loisel & Sergey Utev, 2018. "Markov Property in Discrete Schur-constant Models," Post-Print hal-01995775, HAL.
    3. Castañer, A. & Claramunt, M.M. & Lefèvre, C. & Loisel, S., 2015. "Discrete Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 343-362.
    4. Claude Lefèvre & Stéphane Loisel, 2013. "On multiply monotone distributions, continuous or discrete, with applications," Post-Print hal-00750562, HAL.
    5. Genest, Christian & Mesfioui, Mhamed & Schulz, Juliana, 2018. "A new bivariate Poisson common shock model covering all possible degrees of dependence," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 202-209.
    6. Chi, Yichun & Yang, Jingping & Qi, Yongcheng, 2009. "Decomposition of a Schur-constant model and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 398-408, June.
    7. Mai, Jan-Frederik & Scherer, Matthias & Shenkman, Natalia, 2013. "Multivariate geometric distributions, (logarithmically) monotone sequences, and infinitely divisible laws," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 457-480.
    8. Jones, M.C. & Marchand, Éric, 2019. "Multivariate discrete distributions via sums and shares," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 83-93.
    9. Claude Lefèvre & Stéphane Loisel & Sergey Utev, 2018. "Markov Property in Discrete Schur-constant Models," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 1003-1012, September.
    10. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
    11. N. Nair & P. Sankaran, 2014. "Modelling lifetimes with bivariate Schur-constant equilibrium distributions from renewal theory," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 331-349, October.
    12. M. Sreehari & R. Vasudeva, 2012. "Characterizations of multivariate geometric distributions in terms of conditional distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 271-286, February.
    13. Ta, Bao Quoc & Van, Chung Pham, 2017. "Some properties of bivariate Schur-constant distributions," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 69-76.
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    Cited by:

    1. Claude Lefèvre & Matthieu Simon, 2021. "Schur-Constant and Related Dependence Models, with Application to Ruin Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 317-339, March.
    2. Lefèvre Claude & Picard Philippe, 2023. "Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-17.

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