Size bias for one and all

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.

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