The Coupon Collector's Problem Revisited: Asymptotics of the Variance
2012 ◽
Vol 44
(1)
◽
pp. 166-195
◽
Keyword(s):
We develop techniques for computing the asymptotics of the first and second moments of the number TN of coupons that a collector has to buy in order to find all N existing different coupons as N → ∞. The probabilities (occurring frequencies) of the coupons can be quite arbitrary. From these asymptotics we obtain the leading behavior of the variance V[TN] of TN (see Theorems 3.1 and 4.4). Then, we combine our results with the general limit theorems of Neal in order to derive the limit distribution of TN (appropriately normalized), which, for a large class of probabilities, turns out to be the standard Gumbel distribution. We also give various illustrative examples.
2012 ◽
Vol 44
(01)
◽
pp. 166-195
◽
1980 ◽
Vol 29
(3-4)
◽
pp. 113-132
◽
2018 ◽
Vol 55
(1)
◽
pp. 115-140
2011 ◽
Vol 141
(7)
◽
pp. 2348-2352
◽
1980 ◽
Vol 12
(02)
◽
pp. 319-349
◽
2014 ◽
Vol 10
(S306)
◽
pp. 351-354
1988 ◽
Vol 7
(4)
◽
pp. 289-307
◽
1966 ◽
Vol 3
(01)
◽
pp. 94-114
◽
Keyword(s):