Central Limit Theorems for Infinite Urn Models
نویسندگان
چکیده
منابع مشابه
Local limit theorems for finite and infinite urn models
Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.
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A classical theorem of Rényi [26] for the number of empty boxes, denoted by μ0(n,M), in a sequence of n random allocations of indistinguishable balls into M boxes with equal probability 1/M , can be stated as follows: If the variance of μ0(n,M) tends to infinity with n then μ0(n,M) is asymptotically normally distributed. This result, seldom stated in this form in the literature, was proved by R...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1989
ISSN: 0091-1798
DOI: 10.1214/aop/1176991268