The number of distinct values of some multiplicity in sequences of geometrically distributed random variables
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In this paper, the authors consider a sequence of n geometric random variables and interpret the outcome as an urn model, and derive asymptotic equivalents for all (centered or uncentered) moments in a fairly automatic way.Abstract:
We consider a sequence of n geometric random variables and interpret the outcome as an urn model. For a given parameter m, we treat several parameters like what is the largest urn containing at least (or exactly) m balls, or how many urns contain at least m balls, etc. Many of these questions have their origin in some computer science problems. Identifying the underlying distributions as (variations of) the extreme value distribution, we are able to derive asymptotic equivalents for all (centered or uncentered) moments in a fairly automatic way.read more
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Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws ∗
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Asymptotics of the Moments of Extreme-Value Related Distribution Functions
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On the variance of the number of occupied boxes
TL;DR: This work derives a simple necessary and sufficient condition for convergence of V"n to a finite limit, thus settling a long-standing question raised by Karlin in the seminal paper of 1967.
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Small counts in the infinite occupancy scheme
Andrew Barbour,Alexander Gnedin +1 more
TL;DR: In this paper, the authors considered the classical occupancy scheme in which balls are thrown independently into infinitely many boxes, with given probability of hitting each of the boxes, and established joint normal approximation, as the number of balls goes to infinity, for the numbers of boxes containing any fixed number of counts, standardized in the natural way, assuming only that the variances of these counts all tend to infinity.
References
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