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Stochastic species abundance models involving special copulas

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  • Huillet, Thierry E.

Abstract

Copulas offer a very general tool to describe the dependence structure of random variables supported by the hypercube. Inspired by problems of species abundances in Biology, we study three distinct toy models where copulas play a key role. In a first one, a Marshall–Olkin copula arises in a species extinction model with catastrophe. In a second one, a quasi-copula problem arises in a flagged species abundance model. In a third model, we study completely random species abundance models in the hypercube as those, not of product type, with uniform margins and singular. These can be understood from a singular copula supported by an inflated simplex. An exchangeable singular Dirichlet copula is also introduced, together with its induced completely random species abundance vector.

Suggested Citation

  • Huillet, Thierry E., 2018. "Stochastic species abundance models involving special copulas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 77-91.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:77-91
    DOI: 10.1016/j.physa.2017.08.021
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    References listed on IDEAS

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    1. McNeil, Alexander J. & Neslehová, Johanna, 2010. "From Archimedean to Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1772-1790, September.
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    Cited by:

    1. Damjana Kokol Bukovv{s}ek & Tomav{z} Kov{s}ir & Blav{z} Mojv{s}kerc & Matjav{z} Omladiv{c}, 2018. "Asymmetric linkages: maxmin vs. reflected maxmin copulas," Papers 1808.07737, arXiv.org, revised Jul 2019.
    2. Damjana Kokol Bukovv{s}ek & Tomav{z} Kov{s}ir & Blav{z} Mojv{s}kerc & Matjav{z} Omladiv{c}, 2018. "Non-exchangeability of copulas arising from shock models," Papers 1808.09698, arXiv.org, revised Jul 2019.

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