带通用优惠券的优惠券收集器问题中小规模子收集的等待时间

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability Pub Date : 2024-01-21 DOI:10.1007/s10959-023-01312-2

Jelena Jocković, Bojana Todić

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引用次数: 0

摘要

我们考虑了经典优惠券收集器问题的一般化，其中可用优惠券集合包括标准优惠券（可作为收集的一部分）和两种具有特殊用途的优惠券：一种可加快收集过程，另一种可减慢收集过程。当标准券的数量趋于无穷大时，我们得到了几个与等待时间相关的渐近结果，这些等待时间直到部分收集的样本被取样为止。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Waiting Time for a Small Subcollection in the Coupon Collector Problem with Universal Coupon

We consider a generalization of the classical coupon collector problem, where the set of available coupons consists of standard coupons (which can be part of the collection), and two coupons with special purposes: one that speeds up the collection process and one that slows it down. We obtain several asymptotic results related to the expectation and the variance of the waiting time until a portion of the collection is sampled, as the number of standard coupons tends to infinity.

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来源期刊

Journal of Theoretical Probability 数学-统计学与概率论

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.