Limit distributions for the problem of collecting pairs

Pavle Mladenović

doi:10.3150/07-BEJ114

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Home > Journals > Bernoulli > Volume 14 > Issue 2 > Article

May 2008 Limit distributions for the problem of collecting pairs

Pavle Mladenović

Bernoulli 14(2): 419-439 (May 2008). DOI: 10.3150/07-BEJ114

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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 $jj, j∈N_n$, is sampled. Exact distributions of some related random variables and their characteristics are also obtained.