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Exchangeable random partitions from max-infinitely-divisible distributions

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  • Stoev, Stilian
  • Wang, Yizao

Abstract

The hitting partitions are random partitions that arise from the investigation of so-called hitting scenarios of max-infinitely-divisible (max-i.d.) distributions. We study a class of max-i.d. laws with exchangeable hitting partitions obtained by size-biased sampling from the jumps of a Lévy subordinator. We obtain explicit formulae for the distributions of these partitions in the case of the multivariate α-logistic and another family of exchangeable max-i.d. distributions. Specifically, the hitting partitions for these two cases are shown to coincide with the well-known Poisson–Dirichlet partitions PD(α,0),α∈(0,1) and PD(0,θ),θ>0.

Suggested Citation

  • Stoev, Stilian & Wang, Yizao, 2019. "Exchangeable random partitions from max-infinitely-divisible distributions," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 50-56.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:50-56
    DOI: 10.1016/j.spl.2018.11.008
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    References listed on IDEAS

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    1. Hashorva, Enkelejd & Hüsler, Jürg, 2005. "Multiple maxima in multivariate samples," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 11-17, November.
    2. Molchanov, Ilya & Strokorb, Kirstin, 2016. "Max-stable random sup-measures with comonotonic tail dependence," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2835-2859.
    3. Alec Stephenson & Jonathan Tawn, 2005. "Exploiting occurrence times in likelihood inference for componentwise maxima," Biometrika, Biometrika Trust, vol. 92(1), pages 213-227, March.
    4. 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.
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    Cited by:

    1. Durieu, Olivier & Wang, Yizao, 2022. "Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 55-88.
    2. Hashorva, Enkelejd & Rullière, Didier, 2020. "Asymptotic domination of sample maxima," Statistics & Probability Letters, Elsevier, vol. 160(C).

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