Title: A central limit theorem for exchangeable variates with geometric applications
Abstract: A central limit theorem is proved for the sum of random variables X r all having the same form of distribution and each of which depends on a parameter which is the number occurring in the r th 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.
Publication Year: 1973
Publication Date: 1973-12-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 8
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