IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v53y1995i2p293-310.html
   My bibliography  Save this article

Parametric Schur Convexity and Arrangement Monotonicity Properties of Partial Sums

Author

Listed:
  • Shaked, M.
  • Shanthikumar, J. G.
  • Tong, Y. L.

Abstract

Studying the joint distributional properties of partial sums of independent random variables, we obtain stochastic analogues of some simple deterministic results from the theory of majorization, Schur-convexity, and arrangement monotonicity. More explicitly, let Xi([theta]i), i =1, ..., n, be independent random variables such that the distribution of Xi([theta]i) is determined by the value of [theta]i. Let S([theta]) = (X1([theta]1), X1([theta]1) + X2([theta]2), ..., [Sigma]ni = 1Xi([theta]i)). We give sufficient conditions on f : n --> and on {Xi([theta]), [theta] [set membership, variant] [Theta]} under which f(S([theta])) have some stochastic arrangement monotonicity and stochastic Schur-convexity properties.

Suggested Citation

  • Shaked, M. & Shanthikumar, J. G. & Tong, Y. L., 1995. "Parametric Schur Convexity and Arrangement Monotonicity Properties of Partial Sums," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 293-310, May.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:2:p:293-310
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(85)71038-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Shaked, Moshe & Shanthikumar, J. George, 1997. "Supermodular Stochastic Orders and Positive Dependence of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 86-101, April.
    2. Wei-Feng Xia & Xiao-Hui Zhan & Gen-Di Wang & Yu-Ming Chu, 2012. "Some properties for a class of symmetric functions with applications," Indian Journal of Pure and Applied Mathematics, Springer, vol. 43(3), pages 227-249, June.
    3. Ma, Chunsheng, 2000. "ISO* Property of Two-Parameter Compound Poisson Distributions with Applications," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 279-294, November.

    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:jmvana:v:53:y:1995:i:2:p:293-310. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.