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.

Limit Laws for the Maximum of Weighted and Shifted I.I.D. Random Variables

D. J. Daley and Peter Hall
The Annals of Probability
Vol. 12, No. 2 (May, 1984), pp. 571-587
Stable URL: http://www.jstor.org/stable/2243488
Page Count: 17
  • 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.
Limit Laws for the Maximum of Weighted and Shifted I.I.D. Random Variables
Preview not available

Abstract

Gnedenko's (1943) study of the class G of limit laws for the sequence of maxima $M_n \equiv \max\{X_0, \cdots, X_{n - 1}\}$ of independent identically distributed random variables X0, X1, ⋯ is extended to limit laws for weighted sequences {wn(γ)Xn} (the simplest case {γnX n} has geometric weights $(0 \leq \gamma < 1))$ and translated sequences {Xn - vn(δ)} (the simplest case is $\{X_n - n\delta\} (\delta > 0))$. Limit laws for these simplest cases belong to the family G characterized by Gnedenko; with more general weights or translates, limit laws outside G may arise.

Page Thumbnails

  • Thumbnail: Page 
571
    571
  • Thumbnail: Page 
572
    572
  • Thumbnail: Page 
573
    573
  • Thumbnail: Page 
574
    574
  • Thumbnail: Page 
575
    575
  • Thumbnail: Page 
576
    576
  • Thumbnail: Page 
577
    577
  • Thumbnail: Page 
578
    578
  • Thumbnail: Page 
579
    579
  • Thumbnail: Page 
580
    580
  • Thumbnail: Page 
581
    581
  • Thumbnail: Page 
582
    582
  • Thumbnail: Page 
583
    583
  • Thumbnail: Page 
584
    584
  • Thumbnail: Page 
585
    585
  • Thumbnail: Page 
586
    586
  • Thumbnail: Page 
587
    587