We extend the classical coupon collector problem to find the expected number of selections needed to collect $m_i$ (possible random) copies of coupon $i$, when the distribution of the coupons is not necessarily equally likely. Upper and lower bounds which provide limiting asymptotics are also obtained for the expected number of selections needed to fulfill a random quota for each coupon.
@article{10_37236_3348,
author = {Nathan B. Shank and Hannah Yang},
title = {Coupon collector problem for non-uniform coupons and random quotas},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {2},
doi = {10.37236/3348},
zbl = {1267.05288},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3348/}
}
TY - JOUR
AU - Nathan B. Shank
AU - Hannah Yang
TI - Coupon collector problem for non-uniform coupons and random quotas
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/3348/
DO - 10.37236/3348
ID - 10_37236_3348
ER -
%0 Journal Article
%A Nathan B. Shank
%A Hannah Yang
%T Coupon collector problem for non-uniform coupons and random quotas
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/3348/
%R 10.37236/3348
%F 10_37236_3348
Nathan B. Shank; Hannah Yang. Coupon collector problem for non-uniform coupons and random quotas. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/3348
