Urns & Tubes

Author:

Jacobs Bart1ORCID

Affiliation:

1. Institute for Computing and Information Sciences, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands

Abstract

Urn models play an important role to express various basic ideas in probability theory. Here we extend this urn model with tubes. An urn contains coloured balls, which can be drawn with probabilities proportional to the numbers of balls of each colour. For each colour a tube is assumed. These tubes have different sizes (lengths). The idea is that after drawing a ball from the urn it is dropped in the tube of the corresponding colour. We consider two associated probability distributions. The first-full distribution on colours gives for each colour the probability that the corresponding tube is full first, before any of the other tubes. The negative distribution on natural numbers captures for a numberkthe probability that all tubes are full for the first time afterkdraws.This paper uses multisets to systematically describe these first-full and negative distributions in the urns and tubes setting, in fully multivariate form, for all three standard drawing modes (multinomial, hypergeometric, and Pólya).

Publisher

Compositionality

Subject

General Medicine

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Element-free probability distributions and random partitions;Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science;2024-07-08

2. Drawing from an Urn is Isometric;Lecture Notes in Computer Science;2024

3. Some Probabilistic Riddles and Some Logical Solutions;Lecture Notes in Computer Science;2024

4. Overdrawing Urns using Categories of Signed Probabilities;Electronic Proceedings in Theoretical Computer Science;2023-12-14

5. A Principled Approach to Expectation Maximisation and Latent Dirichlet Allocation Using Jeffrey’s Update Rule;Logic, Language, Information, and Computation;2023

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3