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Markov Property in Discrete Schur-constant Models

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Abstract

This paper is concerned with Schur-constant survival models for discrete random variables. Our main purpose is to prove that the associated partial sum process is a non-homogeneous Markov chain. This is shown in three different situations where the random variables considered take values in the sets 0, {0,1} or {0,…,m}, m ≥ 2. The property of Schur-constancy is also compared for these three cases.

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References

  • Barlow RE, Mendel MB (1993) Similarity as a probabilistic characteristic of aging. In: Clarotti CE, Barlow RE, Spizzichino F (eds) Reliability and decision making. Chapman and Hall, London, pp 233–244

    Chapter  Google Scholar 

  • Caramellino L, Spizzichino F (1994) Dependence and aging properties of lifetimes with Schur-constant survival function. Probab Eng Inf Sci 8:103–111

    Article  Google Scholar 

  • Castañer A, Claramunt M M, Lefèvre C, Loisel S (2015) Discrete Schur-constant models. J Multivar Anal 140:343–362

    Article  MathSciNet  MATH  Google Scholar 

  • Chi Y, Yang J, Qi Y (2009) Decomposition of a Schur-constant model and its applications. Insur Math Econ 44:398–408

    Article  MathSciNet  MATH  Google Scholar 

  • Lefèvre C, Loisel S, Utev S (2017) On finite exchangeable sequences and their dependence. Submitted

  • Nair N U, Sankaran P G (2014) Characterizations and time-dependent association measures for bivariate Schur-constant distributions. Braz J Probab Stat 28:409–423

    Article  MathSciNet  MATH  Google Scholar 

  • Nelsen RB (2005) Some properties of Schur-constant survival models and their copulas. Braz J Probab Stat 19:179–190

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

We thank the referee for valuable comments and suggestions. C. L. received support from the Chair Generali Actuariat Responsable sponsored by the French Fondation du Risque. S. L. received support from the Research Project LoLitA of the French Agence Nationale de la Recherche, and the Chair Actuariat Durable sponsored by Milliman. The research of S. U. was funded by a Mission Scientifique of the Belgian FNRS.

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Authors and Affiliations

  1. Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, 1050, Bruxelles, Belgium

    Claude Lefèvre

  2. Institut de Science Financière et d’Assurances, Université de Lyon, 50 Avenue Tony Garnier, 69007, Lyon, France

    Claude Lefèvre & Stéphane Loisel

  3. Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, UK

    Sergey Utev

Authors
  1. Claude Lefèvre
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  2. Stéphane Loisel
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  3. Sergey Utev
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Correspondence to Claude Lefèvre.

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Lefèvre, C., Loisel, S. & Utev, S. Markov Property in Discrete Schur-constant Models. Methodol Comput Appl Probab 20, 1003–1012 (2018). https://doi.org/10.1007/s11009-017-9564-5

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  • DOI: https://doi.org/10.1007/s11009-017-9564-5

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