IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v83y2016i3d10.1007_s00186-015-0530-0.html
   My bibliography  Save this article

On the extreme points of moments sets

Author

Listed:
  • Iosif Pinelis

    (Michigan Technological University)

Abstract

Necessary and sufficient conditions for a measure to be an extreme point of the set of measures on a given measurable space with prescribed generalized moments are given, as well as an application to extremal problems over such moment sets; these conditions are expressed in terms of atomic partitions of the measurable space. It is also shown that every such extreme measure can be adequately represented by a linear combination of k Dirac probability measures with nonnegative coefficients, where k is the number of restrictions on moments; moreover, when the measurable space has appropriate topological properties, the phrase “can be adequately represented by” here can be replaced simply by “is”. Applications to specific extremal problems are also given, including an exact lower bound on the exponential moments of truncated random variables, exact lower bounds on generalized moments of the interarrival distribution in queuing systems, and probability measures on product spaces with prescribed generalized marginal moments.

Suggested Citation

  • Iosif Pinelis, 2016. "On the extreme points of moments sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(3), pages 325-349, June.
  • Handle: RePEc:spr:mathme:v:83:y:2016:i:3:d:10.1007_s00186-015-0530-0
    DOI: 10.1007/s00186-015-0530-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-015-0530-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00186-015-0530-0?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. Tyner, Wally & Adams, John, 1976. "Rural Electrification In India: Biogas Versus Large Scale Power," 1976 Annual Meeting, August 15-18, State College, Pennsylvania 283822, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    2. Ward Whitt, 1983. "Untold Horrors of the Waiting Room: What the Equilibrium Distribution Will Never Tell About the Queue-Length Process," Management Science, INFORMS, vol. 29(4), pages 395-408, April.
    3. A. E. Eckberg, 1977. "Sharp Bounds on Laplace-Stieltjes Transforms, with Applications to Various Queueing Problems," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 135-142, May.
    4. Gerhard Winkler, 1988. "Extreme Points of Moment Sets," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 581-587, November.
    5. Alan F. Karr, 1983. "Extreme Points of Certain Sets of Probability Measures, with Applications," Mathematics of Operations Research, INFORMS, vol. 8(1), pages 74-85, February.
    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. Amparo Ba'illo & Javier C'arcamo & Carlos Mora-Corral, 2021. "Extremal points of Lorenz curves and applications to inequality analysis," Papers 2103.03286, arXiv.org.

    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. Henry Lam & Clementine Mottet, 2017. "Tail Analysis Without Parametric Models: A Worst-Case Perspective," Operations Research, INFORMS, vol. 65(6), pages 1696-1711, December.
    2. Juan González-Hernández & César Villarreal, 2011. "Optimal policies for constrained average-cost Markov decision processes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 107-120, July.
    3. Hansjörg Albrecher & José Carlos Araujo-Acuna, 2022. "On The Randomized Schmitter Problem," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 515-535, June.
    4. Bergemann, Dirk & Castro, Francisco & Weintraub, Gabriel Y., 2020. "The scope of sequential screening with ex post participation constraints," Journal of Economic Theory, Elsevier, vol. 188(C).
    5. Chien-Yu Lai & Andreas Lange & John A. List & Michael K. Price, 2017. "The Business of Business is Business: Why (Some) Firms Should Provide Public Goods when they Sell Private Goods," NBER Working Papers 23105, National Bureau of Economic Research, Inc.
    6. Wouter van Eekelen & Dick den Hertog & Johan S.H. van Leeuwaarden, 2022. "MAD Dispersion Measure Makes Extremal Queue Analysis Simple," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1681-1692, May.
    7. Herweg, Fabian & Rosato, Antonio, 2018. "Bait and Ditch: Consumer Naiveté and Salesforce Incentives," CEPR Discussion Papers 12612, C.E.P.R. Discussion Papers.
    8. Riis, Morten & Andersen, Kim Allan, 2005. "Applying the minimax criterion in stochastic recourse programs," European Journal of Operational Research, Elsevier, vol. 165(3), pages 569-584, September.
    9. Freeman, Mark C. & Groom, Ben, 2016. "How certain are we about the certainty-equivalent long term social discount rate?," Journal of Environmental Economics and Management, Elsevier, vol. 79(C), pages 152-168.
    10. Mark Armstrong, 2016. "Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 583-614, October.
    11. Kai Hao Yang & Alexander K. Zentefis, 2023. "Extreme Points of First-Order Stochastic Dominance Intervals: Theory and Applications," Cowles Foundation Discussion Papers 2355, Cowles Foundation for Research in Economics, Yale University.
    12. Heski Bar‐Isaac & Guillermo Caruana & Vicente Cuñat, 2010. "Information Gathering and Marketing," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(2), pages 375-401, June.
    13. Thi Thuy Hang NGUYEN, 2016. "The United States and the European Community, 1969-1974: an uneasy partnership," Eastern Journal of European Studies, Centre for European Studies, Alexandru Ioan Cuza University, vol. 7, pages 169-184, June.
    14. Alexander Schied, 2004. "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals," Papers math/0407127, arXiv.org.
    15. Becker, Gary S & Tomes, Nigel, 1976. "Child Endowments and the Quantity and Quality of Children," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 143-162, August.
    16. Gregory S. Crawford, 2015. "The economics of television and online video markets," ECON - Working Papers 197, Department of Economics - University of Zurich.
    17. Baligh, Helmy H., 1998. "The fit between the organization structure and its cultural setting: aspects of Islamic cultures," International Business Review, Elsevier, vol. 7(1), pages 39-49, February.
    18. Sang‐Hyun Kim & Jong‐Hee Hahn, 2022. "On the profitability of interfirm bundling in oligopolies," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 31(3), pages 657-673, August.
    19. Michael Kupper & Max Nendel & Alessandro Sgarabottolo, 2023. "Risk measures based on weak optimal transport," Papers 2312.05973, arXiv.org.
    20. Xu Jia & Liu Liwei & Zhu Taozeng, 2018. "Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 69-84, February.

    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:spr:mathme:v:83:y:2016:i:3:d:10.1007_s00186-015-0530-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.