Distributions in the constant-differentials Pólya process

Hosam M. Mahmoud and Panpan Zhang

Statistics & Probability Letters, 2020, vol. 156, issue C

Abstract: We study a class of unbalanced constant-differentials Pólya processes on white and blue balls. We show that the number of white balls, the number of blue balls, and the total number of balls, when appropriately scaled, all converge in distribution to gamma random variables with parameters depending on the differential index and the amount of ball addition at the epochs, but not on the initial conditions. The result is obtained by an analytic approach utilizing partial differential equations. We present a martingale formulation that may provide alternatives.

Keywords: Pólya urn; Pólya process; Partial differential equation; Method of characteristic curves; Transport equation; Continuous-time martingale (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016771521930238X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:156:y:2020:i:c:s016771521930238x

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2019.108592

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 ().