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Modelling lifetimes with bivariate Schur-constant equilibrium distributions from renewal theory

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  • N. Nair

  • P. Sankaran

Abstract

In the present work we study the asymptotic distribution of the age and residual life in a renewal process. The bivariate distribution so derived is Schur-constant with marginal distributions as equilibrium discuss the reliability properties and the copula. The bivariate ageing properties and some stochastic orders connecting them are explored. It is shown that various time dependent measures of association and dependence concepts can be inferred from the ageing properties of the baseline distribution. Copyright Sapienza Università di Roma 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metron:v:72:y:2014:i:3:p:331-349
    DOI: 10.1007/s40300-014-0045-0
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    References listed on IDEAS

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    1. Hu, Taizhong & Khaledi, Baha-Eldin & Shaked, Moshe, 2003. "Multivariate hazard rate orders," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 173-189, January.
    2. Abouammoh, A. M. & Ahmad, R. & Khalique, A., 2000. "On new renewal better than used classes of life distributions," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 189-194, June.
    3. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
    4. Caramellino, Lucia & Spizzichino, Fabio, 1996. "WBF Property and Stochastical Monotonicity of the Markov Process Associated to Schur-Constant Survivial Functions," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 153-163, January.
    5. Nair, N. Unnikrishnan & Preeth, M., 2008. "Multivariate equilibrium distributions of order n," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3312-3320, December.
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    Cited by:

    1. 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.
    2. Anna Casta~ner & M Merc`e Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Papers 1709.09955, arXiv.org.
    3. Anna Castañer & M Mercè Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Working Papers hal-01593552, HAL.
    4. 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.

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