Dynamic Pólya–Eggenberger urns
Yarong Feng and
Hosam M. Mahmoud
Statistics & Probability Letters, 2021, vol. 174, issue C
We study types of Pólya-Eggenberger urn schemes with a dynamic replacement matrix. We consider two-color schemes (white and blue) in this class. The nature of the governing limit stochastic relation exhibits a phase change when the addition function meets a regularity condition. We show that when the condition is met, the proportion of white balls in such an urn converges to a Bernoulli limit distribution. This is to be contrasted with dynamic Pólya-Eggenberger urns with slow addition function, where the limit distribution is believed to be continuous on the interval [0,1]. We demonstrate that the condition is satisfied when the addition function, along a subsequence of draws, grows exponentially (the exponential Pólya-Eggenberger urn) or faster (the super exponential Pólya-Eggenberger urn).
Keywords: Urn model; Random structure; Martingale; Limit distribution (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
Full text for ScienceDirect subscribers only
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:174:y:2021:i:c:s0167715221000511
Ordering information: This journal article can be ordered from
https://shop.elsevie ... _01_ooc_1&version=01
Access Statistics for this article
Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul
More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().