Statistics and Its Interface

Volume 7 (2014)

Number 3

Special Issue on Extreme Theory and Application (Part I)

Guest Editors: Yazhen Wang and Zhengjun Zhang

Coupon collector’s problem and its extensions in extreme value framework

Pages: 381 – 388

DOI: https://dx.doi.org/10.4310/SII.2014.v7.n3.a8

Authors

Jelena Jockovic (Faculty of Pharmacy, University of Belgrade, Serbia)

Pavle Mladenovic (Faculty of Mathematics, University of Belgrade, Serbia)

Abstract

Let $\mathbb{N}_n = \{ 1, 2, \dots , n \}$.We sample with replacement from the set $\mathbb{N}_n$, assuming that each element has the same probability of being drawn. We determine the limiting distributions and some related properties of the waiting time $M_n$ until all triples $j j j , j \in \mathbb{N}_n$ are sampled.

Keywords

extreme values, limit theorems, waiting time, excesses over the threshold, recurrence relation

Published 9 September 2014