Limit distributions for the problem of collecting pairs

Pavle Mladenović

doi:10.3150/07-BEJ114

paper

Limit distributions for the problem of collecting pairs

arXiv:0805.2041 · doi:10.3150/07-BEJ114

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 $j j$ , $j \in N_{n}$ , is sampled. Exact distributions of some related random variables and their characteristics are also obtained.

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)