If you need an accessible version of this item please contact JSTOR User Support

Poisson Approximation for Dependent Trials

Louis H. Y. Chen
The Annals of Probability
Vol. 3, No. 3 (Jun., 1975), pp. 534-545
Stable URL: http://www.jstor.org/stable/2959474
Page Count: 12
  • Download PDF
  • Cite this Item

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 need an accessible version of this item please contact JSTOR User Support
Poisson Approximation for Dependent Trials
Preview not available

Abstract

Let $X_1, \cdots, X_n$ be an arbitrary sequence of dependent Bernoulli random variables with $P(X_i = 1) = 1 - P(X_i = 0) = p_i.$ This paper establishes a general method of obtaining and bounding the error in approximating the distribution of $\sum^n_{i=1} X_i$ by the Poisson distribution. A few approximation theorems are proved under the mixing condition of Ibragimov (1959), (1962). One of them yields, as a special case and with some improvement, an approximation theorem of Le Cam (1960) for the Poisson binomial distribution. The possibility of an asymptotic expansion is also discussed and a refinement in the independent case obtained. The method is similar to that of Charles Stein (1970) in his paper on the normal approximation for dependent random variables.

Page Thumbnails

  • Thumbnail: Page 
534
    534
  • Thumbnail: Page 
535
    535
  • Thumbnail: Page 
536
    536
  • Thumbnail: Page 
537
    537
  • Thumbnail: Page 
538
    538
  • Thumbnail: Page 
539
    539
  • Thumbnail: Page 
540
    540
  • Thumbnail: Page 
541
    541
  • Thumbnail: Page 
542
    542
  • Thumbnail: Page 
543
    543
  • Thumbnail: Page 
544
    544
  • Thumbnail: Page 
545
    545