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.

Compound Poisson Approximations for the Numbers of Extreme Spacings

Małgorzata Roos
Advances in Applied Probability
Vol. 25, No. 4 (Dec., 1993), pp. 847-874
DOI: 10.2307/1427795
Stable URL: http://www.jstor.org/stable/1427795
Page Count: 28
  • 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.
Compound Poisson Approximations for the Numbers of Extreme Spacings
Preview not available

Abstract

The accuracy of the Poisson approximation to the distribution of the numbers of large and small m-spacings, when n points are placed at random on the circle, was analysed using the Stein-Chen method in Barbour et al. (1992b). The Poisson approximation for m≥ 2 was found not to be as good as for 1-spacings. In this paper, rates of approximation of these distributions to suitable compound Poisson distributions are worked out, using the CP-Stein-Chen method and an appropriate coupling argument. The rates are better than for Poisson approximation for m≥ 2, and are of order O((log n)2/n) for large m-spacings and of order O(1/n) for small m-spacings, for any fixed m≥ 2, if the expected number of spacings is held constant as n→ ∞ .

Page Thumbnails

  • Thumbnail: Page 
847
    847
  • Thumbnail: Page 
848
    848
  • Thumbnail: Page 
849
    849
  • Thumbnail: Page 
850
    850
  • Thumbnail: Page 
851
    851
  • Thumbnail: Page 
852
    852
  • Thumbnail: Page 
853
    853
  • Thumbnail: Page 
854
    854
  • Thumbnail: Page 
855
    855
  • Thumbnail: Page 
856
    856
  • Thumbnail: Page 
857
    857
  • Thumbnail: Page 
858
    858
  • Thumbnail: Page 
859
    859
  • Thumbnail: Page 
860
    860
  • Thumbnail: Page 
861
    861
  • Thumbnail: Page 
862
    862
  • Thumbnail: Page 
863
    863
  • Thumbnail: Page 
864
    864
  • Thumbnail: Page 
865
    865
  • Thumbnail: Page 
866
    866
  • Thumbnail: Page 
867
    867
  • Thumbnail: Page 
868
    868
  • Thumbnail: Page 
869
    869
  • Thumbnail: Page 
870
    870
  • Thumbnail: Page 
871
    871
  • Thumbnail: Page 
872
    872
  • Thumbnail: Page 
873
    873
  • Thumbnail: Page 
874
    874