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A central limit theorem for exchangeable variates with geometric applications

Published online by Cambridge University Press:  14 July 2016

P. A. P. Moran
P. A. P. Moran*
Affiliation:
The Australian National University
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Abstract

A central limit theorem is proved for the sum of random variables Xr all having the same form of distribution and each of which depends on a parameter which is the number occurring in the rth cell of a multinomial distribution with equal probabilities in N cells and a total n, where nN–1 tends to a non-zero constant. This result is used to prove the asymptotic normality of the distribution of the fractional volume of a large cube which is not covered by N interpenetrating spheres whose centres are at random, and for which NV–1 tends to a non-zero constant. The same theorem can be used to prove asymptotic normality for a large number of occupancy problems.

Keywords

CENTRAL LIMIT THEOREMEXCHANGEABLE VARIABLESGEOMETRIC PROBABILITYOCCUPANCY
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 837 - 846
Copyright
Copyright © Applied Probability Trust 1973 

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