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Equilibrium distributions and discrete Schur-constant models

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  • Anna Casta~ner
  • M Merc`e Claramunt

Abstract

This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, the bivariate case is considered and analyzed in depth, stressing the main characteristics of the Poisson case. The analysis is then extended to the multivariate case. Several properties are derived, including the implicit correlation and the distribution of the sum.

Suggested Citation

  • Anna Casta~ner & M Merc`e Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Papers 1709.09955, arXiv.org.
    • Handle: RePEc:arx:papers:1709.09955
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    References listed on IDEAS

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    1. 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.
    2. Sreenarayanapurath Madhavan Sunoj, 2004. "Characterizations of some continuous distributions using partial moments," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 353-362.
    3. Lefèvre, Claude & Loisel, Stéphane, 2010. "Stationary-excess operator and convex stochastic orders," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 64-75, August.
    4. 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.
    5. Claude Lefèvre & Stéphane Loisel, 2013. "On multiply monotone distributions, continuous or discrete, with applications," Post-Print hal-00750562, HAL.
    6. Ta, Bao Quoc & Van, Chung Pham, 2017. "Some properties of bivariate Schur-constant distributions," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 69-76.
    7. 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.
    8. repec:cup:astinb:v:12:y:1981:i:01:p:22-26_00 is not listed on IDEAS
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