Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

'Wald's Lemma' for Sums of Order Statistics of i.i.d. Random Variables

F. Thomas Bruss and James B. Robertson
Advances in Applied Probability
Vol. 23, No. 3 (Sep., 1991), pp. 612-623
DOI: 10.2307/1427625
Stable URL: http://www.jstor.org/stable/1427625
Page Count: 12
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
'Wald's Lemma' for Sums of Order Statistics of i.i.d. Random Variables
Preview not available

Abstract

Let X1,X2,⋯ ,Xn be positive i.i.d. random variables with known distribution function having a finite mean. For a given $s>0$ we define Nn=N(n,s) to be the largest number k such that the sum of the smallest k Xs does not exceed s, and Mn=M(n,s) to be the largest number k such that the sum of the largest k X's does not exceed s. This paper studies the precise and asymptotic behaviour of E(Nn), E(Mn), Nn, Mn, and the corresponding 'stopped' order statistics X(Nn) and X(n-Mn+1) as n→ ∞ , both for fixed s, and where s=sn is an increasing function of n.

Page Thumbnails

  • Thumbnail: Page 
612
    612
  • Thumbnail: Page 
613
    613
  • Thumbnail: Page 
614
    614
  • Thumbnail: Page 
615
    615
  • Thumbnail: Page 
616
    616
  • Thumbnail: Page 
617
    617
  • Thumbnail: Page 
618
    618
  • Thumbnail: Page 
619
    619
  • Thumbnail: Page 
620
    620
  • Thumbnail: Page 
621
    621
  • Thumbnail: Page 
622
    622
  • Thumbnail: Page 
623
    623