Abstract
We investigate the maximal number M
k
of offspring amongst all individuals in a critical Galton-Watson process started with k ancestors. We show that when the reproduction law has a regularly varying tail with index -α for 1 < α < 2, then k
-1
M
k
converges in distribution to a Frechet law with shape parameter 1 and scale parameter depending only on α.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
4 articles.
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