Limit distributions for the problem of collecting pairs

Details Limit distributions for the problem of collecting pairs Limit distributions for the problem of collecting pairs

2008-05-14

arxiv.org/abs/0805.2041v1

Bernoulli 2008, Vol. 14, No. 2, 419-439

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/07-BEJ114 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/07-BEJ114

Let $N_n=\{1,2,...,n\}$. Elements are drawn from the set $N_n$ with
replacement, assuming that each element has probability $1/n$ of being drawn.
We determine the limiting distributions for the waiting time until the given
portion of pairs $jj$, $j\in N_n$, is sampled. Exact distributions of some
related random variables and their characteristics are also obtained.

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