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Size bias for one and all. (English) Zbl 1427.60002
Summary: 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, branching processes, and number theory. In this paper we review the basics and survey some of these unexpected connections.

MSC:
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60E05 Probability distributions: general theory
60G42 Martingales with discrete parameter
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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