Asymptotics for the random coupon collector problem
نویسندگان
چکیده
منابع مشابه
Coupon Collector Problem for Non-Uniform Coupons and Random Quotas
We extend the classical coupon collector problem to find the expected number of selections needed to collect mi (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.
متن کاملThe Coupon-Collector Problem Revisited
A standard combinatorial problem calls to cstlmate the expected number of purchases of coupons needed LO complete Ute collection of all possible m different types. Generalizing this problem. by letting lhe coupons be obtained with an arbitrary probability distribution. and considering other related processes, the problem has been found to model many practical siwations. The usefulness of lhis m...
متن کاملThe Generalized Coupon Collector Problem
Coupons are collected one at a time from a population containing n distinct types of coupon. The process is repeated until all n coupon have been collected and the total number of draws, Y , from the population is recorded. It is assumed that the draws from the population are independent and identically distributed (draws with replacement) according to a probability distribution X with the prob...
متن کاملThe Generalised Coupon Collector Problem
Coupons are collected one at a time from a population containing n distinct types of coupon. The process is repeated until all n coupons have been collected and the total number of draws, Y , from the population is recorded. It is assumed that the draws from the population are independent and identically distributed (draws with replacement) according to a probability distributionXwith the proba...
متن کاملA Generalized Coupon Collector Problem
This paper provides analysis to a generalized version of the coupon collector problem, in which the collector gets d coupons each run and he chooses the one that he has the least so far. In the asymptotic case when the number of coupons n goes to infinity, we show that on average n log n d + n d (m−1) log log n+O(mn) runs are needed to collect m sets of coupons. An efficient exact algorithm is ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1998
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00058-2