Size bias for one and all
Probability
2018-09-28 v3
Abstract
Size bias occurs famously in waiting-time paradoxes, undesirably in sampling schemes, and unexpectedly in connection with Stein's method, tightness, analysis of the lognormal distribution, Skorohod embedding, infinite divisibility, and number theory. In this paper we review the basics and survey some of these unexpected connections.
Cite
@article{arxiv.1308.2729,
title = {Size bias for one and all},
author = {Richard Arratia and Larry Goldstein and Fred Kochman},
journal= {arXiv preprint arXiv:1308.2729},
year = {2018}
}
Comments
New version is 57 pages. There is a new section 7, on Martingale size bias, and size bias for Galton Watson trees. Older: 42 pages, 1 figure. Removed 2 conjectures from the section "Size bias, the lognormal, and Chihara--Leipnik", thanks to information from Christian Berg. Added a new section on Palm measures