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Stochastic decomposition for ℓp-norm symmetric survival functions on the positive orthant

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  • Mai, Jan-Frederik
  • Wang, Ruodu

Abstract

We derive a stochastic representation for the probability distribution on the positive orthant (0,∞)d whose association between components is minimal among all probability laws with ℓp-norm symmetric survival functions. It is given by a transformation of a uniform distribution on the standard unit simplex that is multiplied with an independent finite mixture of certain beta distributions and an additional atom at unity. On the one hand, this implies an efficient simulation algorithm for arbitrary probability laws with ℓp-norm symmetric survival function. On the other hand, this result is leveraged to construct an exact simulation algorithm for max-infinitely divisible probability distributions on the positive orthant whose exponent measure has ℓp-norm symmetric survival function. Both applications generalize existing results for the case p=1 to the case of arbitrary p≥1.

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  • Mai, Jan-Frederik & Wang, Ruodu, 2021. "Stochastic decomposition for ℓp-norm symmetric survival functions on the positive orthant," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jmvana:v:184:y:2021:i:c:s0047259x21000385
    DOI: 10.1016/j.jmva.2021.104760
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    1. Charpentier, A. & Fougères, A.-L. & Genest, C. & Nešlehová, J.G., 2014. "Multivariate Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 118-136.
    2. Gneiting, Tilmann, 1999. "Radial Positive Definite Functions Generated by Euclid's Hat," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 88-119, April.
    3. Hofert, Marius & Huser, Raphaël & Prasad, Avinash, 2018. "Hierarchical Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 195-211.
    4. Clément Dombry & Sebastian Engelke & Marco Oesting, 2016. "Exact simulation of max-stable processes," Biometrika, Biometrika Trust, vol. 103(2), pages 303-317.
    5. Mai, Jan-Frederik, 2018. "Exact simulation of reciprocal Archimedean copulas," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 68-73.
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