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February, 1965 Poisson Limits of Multivariate Run Distributions
Carol E. Fuchs, H. T. David
Ann. Math. Statist. 36(1): 215-225 (February, 1965). DOI: 10.1214/aoms/1177700284


$n$ balls on a circle are colored white or black according to $n$ mutually independent binomial trials. It is shown here that, when their expectations converge with $n$, (a) counts of runs of various lengths are asymptotically independent Poisson; (b) counts of certain configurations other than runs yield asymptotic correlated Poisson distributions; (c) counts of configurations with structure independent of $n$ can be partitioned into equivalence classes, with asymptotic equivalence (equality with probability one) and asymptotic independence respectively within and among classes. It is also shown that (d) there cannot, essentially, exist configurations whose counts, asymptotically, are marginally, but not multivariate, Poisson.


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Carol E. Fuchs. H. T. David. "Poisson Limits of Multivariate Run Distributions." Ann. Math. Statist. 36 (1) 215 - 225, February, 1965.


Published: February, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0144.40505
MathSciNet: MR173329
Digital Object Identifier: 10.1214/aoms/1177700284

Rights: Copyright © 1965 Institute of Mathematical Statistics

Vol.36 • No. 1 • February, 1965
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