Some new aspects for the random coupon collector's problem

Alea, Lat
2014 Am. J. Probab. Math. Stat   unpublished
Let T N be the number of coupons that a collector has to buy in order to find all N existing different coupons. The probabilities p n (occurring frequencies) of the coupons are taken to be identically distributed random variables. We develop techniques of computing the asymptotics of the expectation of T N (T N + 1), where X denotes average, given the p n 's. Using these asymptotics we derive the leading behavior of the expectation of V (T N), where V (T N) is the variance of T N , given the p
more » ... T N , given the p n 's (see Theorems 3.1 and 3.2). We also conjecture on the minimum of this quantity.