IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i8p985-991.html

Distribution functions of linear combinations of lattice polynomials from the uniform distribution

Author

Listed:
  • Marichal, Jean-Luc
  • Kojadinovic, Ivan

Abstract

We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which include weighted sums, linear combinations of order statistics, and lattice polynomials, are actually those continuous functions that reduce to linear functions on each simplex of the standard triangulation of the unit cube. They are mainly used in aggregation theory, combinatorial optimization, and game theory, where they are known as discrete Choquet integrals and Lovász extensions.

Suggested Citation

  • Marichal, Jean-Luc & Kojadinovic, Ivan, 2008. "Distribution functions of linear combinations of lattice polynomials from the uniform distribution," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 985-991, June.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:8:p:985-991
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00351-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. E. Algaba & J.M. Bilbao & J.R. Fernández & A. Jiménez, 2004. "The Lovász Extension of Market Games," Theory and Decision, Springer, vol. 56(1), pages 229-238, April.
    2. Michel Grabisch & Jean-Luc Marichal & Marc Roubens, 2000. "Equivalent Representations of Set Functions," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 157-178, May.
    3. Marichal, Jean-Luc, 2006. "Cumulative distribution functions and moments of lattice polynomials," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1273-1279, July.
    Full references (including those not matched with items on IDEAS)

    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. Michel Grabisch & Éric Raufaste, 2008. "An empirical study of statistical properties of Choquet and Sugeno integrals," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445168, HAL.
    2. Ulrich Faigle & Michel Grabisch, 2019. "Least Square Approximations and Linear Values of Cooperative Game," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381231, HAL.
    3. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2018. "An axiomatisation of the Banzhaf value and interaction index for multichoice games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381119, HAL.
    4. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2018. "On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application," European Journal of Operational Research, Elsevier, vol. 271(1), pages 120-140.
    5. Michel Grabisch & Agnieszka Rusinowska, 2020. "k -additive upper approximation of TU-games," PSE-Ecole d'économie de Paris (Postprint) halshs-02860802, HAL.
    6. Ulrich Faigle & Michel Grabisch, 2016. "Bases and linear transforms of TU-games and cooperation systems," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 875-892, November.
    7. Casajus, André & Kramm, Michael & Wiese, Harald, 2020. "Asymptotic stability in the Lovász-Shapley replicator dynamic for cooperative games," Journal of Economic Theory, Elsevier, vol. 186(C).
    8. Kojadinovic, Ivan, 2004. "Estimation of the weights of interacting criteria from the set of profiles by means of information-theoretic functionals," European Journal of Operational Research, Elsevier, vol. 155(3), pages 741-751, June.
    9. Fabien Lange & László Kóczy, 2013. "Power indices expressed in terms of minimal winning coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 281-292, July.
    10. Michel Grabisch & Christophe Labreuche, 2016. "A note on the Sobol' indices and interactive criteria," Documents de travail du Centre d'Economie de la Sorbonne 16003, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    11. Dukhovny, Alexander, 2007. "Lattice polynomials of random variables," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 989-994, June.
    12. Kun Zhou & Zaiwu Gong & Xiaoqing Chen & Roman Słowiński, 2024. "Determination of a Representative Collective Value Function Through a Value Function-Based Consensus-Reaching Process," Group Decision and Negotiation, Springer, vol. 33(5), pages 1089-1113, October.
    13. Kojadinovic, Ivan, 2005. "Relevance measures for subset variable selection in regression problems based on k-additive mutual information," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1205-1227, June.
    14. Frédéric Chantreuil & Sébastien Courtin & Kevin Fourrey & Isabelle Lebon, 2019. "A note on the decomposability of inequality measures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 283-298, August.
    15. Ulrich Faigle & Michel Grabisch, 2015. "Least Square Approximations and Conic Values of Cooperative Games," Documents de travail du Centre d'Economie de la Sorbonne 15047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    16. Gilbert, Hugo & Ouaguenouni, Mohamed & Öztürk, Meltem & Spanjaard, Olivier, 2025. "Robust ordinal regression for subsets comparisons with interactions," European Journal of Operational Research, Elsevier, vol. 320(1), pages 146-159.
    17. Kusunoki, Yoshifumi & Tanino, Tetsuzo, 2017. "Investigation on irreducible cost vectors in minimum cost arborescence problems," European Journal of Operational Research, Elsevier, vol. 261(1), pages 214-221.
    18. Ulrich Faigle & Michel Grabisch, 2014. "Bases and Linear Transforms of Cooperation Systems," Documents de travail du Centre d'Economie de la Sorbonne 14010r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised May 2015.
    19. Faigle, U. & Grabisch, M. & Heyne, M., 2010. "Monge extensions of cooperation and communication structures," European Journal of Operational Research, Elsevier, vol. 206(1), pages 104-110, October.
    20. E. Borgonovo & C. L. Smith, 2011. "A Study of Interactions in the Risk Assessment of Complex Engineering Systems: An Application to Space PSA," Operations Research, INFORMS, vol. 59(6), pages 1461-1476, December.

    More about this item

    Statistics

    Access and download statistics

    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:stapro:v:78:y:2008:i:8:p:985-991. 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.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.