Local limit theorems for finite and infinite urn models
نویسندگان
چکیده
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.
منابع مشابه
1 8 A pr 2 00 6 Local limit theorems for finite and infinite urn models
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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تاریخ انتشار 2006