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On the relationships between copulas of order statistics and marginal distributions

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  • Navarro, Jorge
  • Spizzichino, Fabio

Abstract

In this paper we study the relationships between copulas of order statistics from heterogeneous samples and the marginal distributions of the parent random variables. Specifically, we study the copula of the order statistics obtained from a general random vector . We show that the copula of the order statistics from only depends on the copula of and on the marginal distributions of X1,X2,...,Xn through an exchangeable copula and the average of the marginal distribution functions. We study in detail some relevant cases.

Suggested Citation

  • Navarro, Jorge & Spizzichino, Fabio, 2010. "On the relationships between copulas of order statistics and marginal distributions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 473-479, March.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:473-479
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    References listed on IDEAS

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    1. Rychlik, Tomasz, 1994. "Distributions and expectations of order statistics for possibly dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 31-42, January.
    2. Avérous, Jean & Genest, Christian & C. Kochar, Subhash, 2005. "On the dependence structure of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 159-171, May.
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    Cited by:

    1. Fuchs, Sebastian & Schmidt, Klaus D., 2021. "On order statistics and Kendall’s tau," Statistics & Probability Letters, Elsevier, vol. 169(C).
    2. Castaño-Martínez, A. & Pigueiras, G. & Sordo, M.A., 2019. "On a family of risk measures based on largest claims," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 92-97.
    3. Lebrun, Régis & Dutfoy, Anne, 2014. "Copulas for order statistics with prescribed margins," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 120-133.
    4. Gupta, Nitin & Misra, Neeraj & Kumar, Somesh, 2015. "Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components," European Journal of Operational Research, Elsevier, vol. 240(2), pages 425-430.
    5. Arnold, Sebastian & Molchanov, Ilya & Ziegel, Johanna F., 2020. "Bivariate distributions with ordered marginals," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    6. Dietz, Markus & Fuchs, Sebastian & Schmidt, Klaus D., 2016. "On order statistics and their copulas," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 165-172.
    7. Bezgina, E. & Burkschat, M., 2019. "On total positivity of exchangeable random variables obtained by symmetrization, with applications to failure-dependent lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 95-109.

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