Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum
Probability
2016-02-16 v2
Abstract
In this paper, we revisit the classical results on the generalized St. Petersburg sums. We determine the limit distribution of the St. Petersburg sum conditioning on its maximum, and we analyze how the limit depends on the value of the maximum. As an application, we obtain an infinite sum representation of the distribution function of the possible semistable limits. In the representation, each term corresponds to a given maximum, in particular this result explains that the semistable behavior is caused by the typical values of the maximum.
Keywords
Cite
@article{arxiv.1308.0521,
title = {Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum},
author = {Gábor Fukker and László Györfi and Péter Kevei},
journal= {arXiv preprint arXiv:1308.0521},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.3150/14-BEJ685 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)