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Sharp bounds on the survival function of exchangeable min-stable multivariate exponential sequences

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  • Mai Jan-Frederik

    (XAIA Investment GmbH, Sonnenstr. 19, 80331 München, Germany)

Abstract

We derive lower and upper bounds for the survival function of an exchangeable sequence of random variables, for which the scaled minimum of each finite subgroup has a univariate exponential distribution. These bounds are sharp in the sense that both bounds themselves are attained by exchangeable sequences of the same kind, for which the (non-scaled) minimum of each subgroup has the same univariate exponential distribution as the original sequence. This result is equivalent to inequalities between infinite-dimensional stable tail dependence functions, which leads to inequalities between multivariate extreme-value copulas. In addition, it is explained how an infinite-dimensional symmetric stable tail dependence function can be obtained from its upper bound by censoring certain distributional information. This technique is applied to derive new parametric families.

Suggested Citation

  • Mai Jan-Frederik, 2024. "Sharp bounds on the survival function of exchangeable min-stable multivariate exponential sequences," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-12.
    • Handle: RePEc:vrs:demode:v:12:y:2024:i:1:p:12:n:1002
    DOI: 10.1515/demo-2023-0110
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    References listed on IDEAS

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    1. Segers, Johan, 2012. "Max-stable models for multivariate extremes," LIDAM Reprints ISBA 2012012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Segers, Johan, 2012. "Max-Stable Models For Multivariate Extremes," LIDAM Discussion Papers ISBA 2012011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Mai, Jan-Frederik, 2018. "Extreme-value copulas associated with the expected scaled maximum of independent random variables," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 50-61.
    4. Ressel, Paul, 2013. "Homogeneous distributions—And a spectral representation of classical mean values and stable tail dependence functions," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 246-256.
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