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Discrete Schur-constant models

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  • Castañer, A.
  • Claramunt, M.M.
  • Lefèvre, C.
  • Loisel, S.

Abstract

This paper introduces a class of Schur-constant survival models, of dimension n, for arithmetic non-negative random variables. Such a model is defined through a univariate survival function that is shown to be n-monotone. Two general representations are obtained, by conditioning on the sum of the n variables or through a doubly mixed multinomial distribution. Several other properties including correlation measures are derived. Three processes in insurance theory are discussed for which the claim interarrival periods form a Schur-constant model.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:343-362
    DOI: 10.1016/j.jmva.2015.06.003
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    References listed on IDEAS

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    1. Albrecher, Hansjörg & Constantinescu, Corina & Loisel, Stephane, 2011. "Explicit ruin formulas for models with dependence among risks," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 265-270, March.
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    8. Gneiting, Tilmann, 1999. "Radial Positive Definite Functions Generated by Euclid's Hat," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 88-119, April.
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    Cited by:

    1. Ta, Bao Quoc & Van, Chung Pham, 2017. "Some properties of bivariate Schur-constant distributions," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 69-76.
    2. Anna Casta~ner & M Merc`e Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Papers 1709.09955, arXiv.org.
    3. Aoudia, Djilali Ait & Marchand, Éric & Perron, François, 2016. "Counts of Bernoulli success strings in a multivariate framework," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 1-10.
    4. Peyhardi, Jean & Fernique, Pierre & Durand, Jean-Baptiste, 2021. "Splitting models for multivariate count data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    5. Anna Castañer & M. Mercè Claramunt, 2019. "Equilibrium Distributions and Discrete Schur-constant Models," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 449-459, June.
    6. 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.
    7. Kolev, Nikolai & Mulinacci, Sabrina, 2022. "New characterizations of bivariate discrete Schur-constant models," Statistics & Probability Letters, Elsevier, vol. 180(C).
    8. Castañer, Anna & Claramunt, M. Mercè & Lefèvre, Claude & Loisel, Stéphane, 2019. "Partially Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 47-58.
    9. Anna Castañer & M Mercè Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Working Papers hal-01593552, HAL.
    10. Jones, M.C. & Marchand, Éric, 2019. "Multivariate discrete distributions via sums and shares," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 83-93.
    11. 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.

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