IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v107y2015icp157-163.html
   My bibliography  Save this article

Limiting behaviour of constrained sums of two variables and the principle of a single big jump

Author

Listed:
  • Lehtomaa, Jaakko

Abstract

This note studies the asymptotic properties of the variable Zd:=X1d|{X1+X2=d}, as d→∞. Here X1 and X2 are non-negative i.i.d. variables with a common twice differentiable density function f. General results concerning the distributional limits of Zd are discussed with various examples.

Suggested Citation

  • Lehtomaa, Jaakko, 2015. "Limiting behaviour of constrained sums of two variables and the principle of a single big jump," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 157-163.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:157-163
    DOI: 10.1016/j.spl.2015.08.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215003089
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.08.017?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. Armendáriz, Inés & Loulakis, Michail, 2011. "Conditional distribution of heavy tailed random variables on large deviations of their sum," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1138-1147, May.
    2. Asmussen, Søren & Klüppelberg, Claudia, 1996. "Large deviations results for subexponential tails, with applications to insurance risk," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 103-125, November.
    3. Mihai Banciu & Prakash Mirchandani, 2013. "Technical Note—New Results Concerning Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 61(4), pages 925-931, August.
    4. Martin A. Lariviere, 2006. "A Note on Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 54(3), pages 602-604, June.
    5. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    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. Lehtomaa, Jaakko & Resnick, Sidney I., 2020. "Asymptotic independence and support detection techniques for heavy-tailed multivariate data," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 262-277.
    2. Søren Asmussen & Jaakko Lehtomaa, 2017. "Distinguishing Log-Concavity from Heavy Tails," Risks, MDPI, vol. 5(1), pages 1-14, February.

    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. Schweizer, Nikolaus & Szech, Nora, 2015. "A quantitative version of Myerson regularity," Working Paper Series in Economics 76, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    2. Schweizer, Nikolaus & Szech, Nora, 2015. "The quantitative view of Myerson regularity," Discussion Papers, Research Unit: Economics of Change SP II 2015-307, WZB Berlin Social Science Center.
    3. Paulo Oliveira & Nuria Torrado, 2015. "On proportional reversed failure rate class," Statistical Papers, Springer, vol. 56(4), pages 999-1013, November.
    4. Mailath, George J. & Nöldeke, Georg, 2006. "Extreme Adverse Selection, Competitive Pricing, and Market Breakdown," Working papers 2006/09, Faculty of Business and Economics - University of Basel.
    5. Mailath, George J. & Nöldeke, Georg, 2008. "Does competitive pricing cause market breakdown under extreme adverse selection?," Journal of Economic Theory, Elsevier, vol. 140(1), pages 97-125, May.
    6. Niu, Baozhuang & Zhang, Jie, 2013. "Price, capacity and concession period decisions of Pareto-efficient BOT contracts with demand uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 53(C), pages 1-14.
    7. Manish Gangwar & Hemant K. Bhargava, 2023. "Pricing on‐demand services: Alternative ways of combining usage and access fees," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 11-27, January.
    8. Sirong Luo & Jianrong Wang, 2017. "A technical note on the dynamic nonstationary inventory-pricing control model with lost sale," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5816-5825, October.
    9. Mandal, Prasenjit & Kaul, Rupali & Jain, Tarun, 2018. "Stocking and pricing decisions under endogenous demand and reference point effects," European Journal of Operational Research, Elsevier, vol. 264(1), pages 181-199.
    10. Gökgür, Burak & Karabatı, Selçuk, 2019. "Dynamic and targeted bundle pricing of two independently valued products," European Journal of Operational Research, Elsevier, vol. 279(1), pages 184-198.
    11. Geoffrey A. Chua & Yan Liu, 2019. "Sensitivity analysis on responsive pricing and production under imperfect demand updating," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 529-546, October.
    12. Chaves, Isaías N. & Ichihashi, Shota, 2024. "Auction timing and market thickness," Games and Economic Behavior, Elsevier, vol. 143(C), pages 161-178.
    13. Ehsan Bolandifar & Tianjun Feng & Fuqiang Zhang, 2018. "Simple Contracts to Assure Supply Under Noncontractible Capacity and Asymmetric Cost Information," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 217-231, May.
    14. Stefanos Leonardos & Costis Melolidakis & Constandina Koki, 2022. "Monopoly pricing in vertical markets with demand uncertainty," Annals of Operations Research, Springer, vol. 315(2), pages 1291-1318, August.
    15. Colombo, Luca & Labrecciosa, Paola, 2012. "A note on pricing with risk aversion," European Journal of Operational Research, Elsevier, vol. 216(1), pages 252-254.
    16. Hezarkhani, Behzad, 2017. "Optimal design of uptime-guarantee contracts under IGFR valuations and convex costs," European Journal of Operational Research, Elsevier, vol. 256(2), pages 556-566.
    17. Mihai Banciu & Prakash Mirchandani, 2013. "Technical Note—New Results Concerning Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 61(4), pages 925-931, August.
    18. Mihai Banciu & Esther Gal-Or & Prakash Mirchandani, 2010. "Bundling Strategies When Products Are Vertically Differentiated and Capacities Are Limited," Management Science, INFORMS, vol. 56(12), pages 2207-2223, December.
    19. Anh Ninh & Zuo‐Jun Max Shen & Martin A. Lariviere, 2020. "Concavity and Unimodality of Expected Revenue Under Discrete Willingness to Pay Distributions," Production and Operations Management, Production and Operations Management Society, vol. 29(3), pages 788-796, March.
    20. Juan Pablo Atal & José Ignacio Cuesta & Felipe González & Cristóbal Otero, 2024. "The Economics of the Public Option: Evidence from Local Pharmaceutical Markets," American Economic Review, American Economic Association, vol. 114(3), pages 615-644, March.

    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:107:y:2015:i:c:p:157-163. 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.