Limit distributions for the problem of collecting pairs

Pavle Mladenović

doi:10.3150/07-BEJ114

Limit distributions for the problem of collecting pairs

Statistics Theory 2008-12-18 v1 Statistics Theory

Authors: Pavle Mladenović

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Abstract

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.

Keywords

probability distribution combinatorial games probability theory

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@article{arxiv.0805.2041,
  title  = {Limit distributions for the problem of collecting pairs},
  author = {Pavle Mladenović},
  journal= {arXiv preprint arXiv:0805.2041},
  year   = {2008}
}

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Published in at http://dx.doi.org/10.3150/07-BEJ114 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

Limit distributions for the problem of collecting pairs

Abstract

Keywords

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