IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v490y2018icp77-91.html
   My bibliography  Save this article

Stochastic species abundance models involving special copulas

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117307458
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2017.08.021?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. McNeil, Alexander J. & Neslehová, Johanna, 2010. "From Archimedean to Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1772-1790, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Philippe Lambert, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 284-286, August.
    2. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 223-256, August.
    3. Di Bernardino Elena & Rullière Didier, 2016. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-20, December.
    4. Hoyle, Edward & Mengütürk, Levent Ali, 2013. "Archimedean survival processes," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 1-15.
    5. Jones, M.C. & Marchand, Éric, 2019. "Multivariate discrete distributions via sums and shares," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 83-93.
    6. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
    7. Hofert, Marius & Vrins, Frédéric, 2013. "Sibuya copulas," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 318-337.
    8. Włodzimierz Wysocki, 2015. "Kendall's tau and Spearman's rho for n -dimensional Archimedean copulas and their asymptotic properties," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 442-459, December.
    9. Hua, Lei, 2015. "Tail negative dependence and its applications for aggregate loss modeling," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 135-145.
    10. Cooray Kahadawala, 2018. "Strictly Archimedean copulas with complete association for multivariate dependence based on the Clayton family," Dependence Modeling, De Gruyter, vol. 6(1), pages 1-18, February.
    11. Chaoubi, Ihsan & Cossette, Hélène & Marceau, Etienne & Robert, Christian Y., 2021. "Hierarchical copulas with Archimedean blocks and asymmetric between-block pairs," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    12. Paul Janssen & Luc Duchateau, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 271-275, August.
    13. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    14. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    15. Sabrina Mulinacci, 2018. "Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 205-236, March.
    16. 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.
    17. Mohammed, Nawaf & Furman, Edward & Su, Jianxi, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 425-436.
    18. Zheng Wei & Seongyong Kim & Boseung Choi & Daeyoung Kim, 2019. "Multivariate Skew Normal Copula for Asymmetric Dependence: Estimation and Application," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 365-387, January.
    19. Paul Embrechts & Marius Hofert, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 263-270, August.
    20. Edward Hoyle & Levent Ali Menguturk, 2011. "Archimedean Survival Processes," Papers 1106.2342, arXiv.org, revised Sep 2012.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:77-91. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.