The siblings of the coupon collector

The 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...

The 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...

The 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...

The Occupancy and Coupon Collector problems

A 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 ...