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.

Bounds for the Distribution Function of a Sum of Independent, Identically Distributed Random Variables

Wassily Hoeffding and S. S. Shrikhande
The Annals of Mathematical Statistics
Vol. 26, No. 3 (Sep., 1955), pp. 439-449
Stable URL: http://www.jstor.org/stable/2236471
Page Count: 11
  • Read Online (Free)
  • Download ($19.00)
  • 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.
Bounds for the Distribution Function of a Sum of Independent, Identically Distributed Random Variables
Preview not available

Abstract

The problem is considered of obtaining bounds for the (cumulative) distribution function of the sum of n independent, identically distributed random variables with k prescribed moments and given ranger. For n = 2 it is shown that the best bounds are attained or arbitrarily closely approach with discrete random varibles which take on at most 2k + 2 values. For nonnegative random variables with given mean, explicit bounds are obtained when n = 2; for arbitrary values of n, bounds are given which are asymptotically best in the "tail" of the distribution. Some of the results contribute to the more general problem of obtaining bounds for the expected values of a given function of independent, identically distributed random variables when the expected values of certain functions of the individual variables are given. Although the results are modest in scope, the authors hope that the paper will draw attention to a problem of both mathematical and statistical interest.

Page Thumbnails

  • Thumbnail: Page 
439
    439
  • Thumbnail: Page 
440
    440
  • Thumbnail: Page 
441
    441
  • Thumbnail: Page 
442
    442
  • Thumbnail: Page 
443
    443
  • Thumbnail: Page 
444
    444
  • Thumbnail: Page 
445
    445
  • Thumbnail: Page 
446
    446
  • Thumbnail: Page 
447
    447
  • Thumbnail: Page 
448
    448
  • Thumbnail: Page 
449
    449