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A Poisson limit theorem for weakly exchangeable events
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- Journal:
- Journal of Applied Probability / Volume 16 / Issue 4 / December 1979
- Published online by Cambridge University Press:
- 14 July 2016, pp. 794-802
- Print publication:
- December 1979
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- Article
- Export citation
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Let Y1, Y2, · ·· be a sequence of independent, identically distributed random variables, g some symmetric 0–1 function of m variables and set
Silverman and Brown (1978) have shown that under certain conditions the statistic
is asymptotically distributed as a Poisson random variable. They then use this result to derive limit distributions for various statistics, useful in the analysis of spatial data. In this paper, it is shown that Silverman and Brown's theorem holds under much weaker assumptions; assumptions which involve only the symmetry of the joint distributions of the Xil…im.
