Tail Probabilities of St. Petersburg Sums, Trimmed Sums, and Their Limit

Springer Science and Business Media LLC - Tập 30 - Trang 1104-1129 - 2016
István Berkes1, László Györfi2, Péter Kevei3
1Institute of Statistics, Graz University of Technology, Graz, Austria
2Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, Hungary
3Center for Mathematical Sciences, Technische Universität München, Garching, Germany

Tóm tắt

We provide exact asymptotics for the tail probabilities $${\mathbb {P}}\{ S_{n,r} > x \}$$ as $$x \rightarrow \infty $$ , for fixed n, where $$S_{n,r}$$ is the r-trimmed partial sum of i.i.d. St. Petersburg random variables. In particular, we prove that although the St. Petersburg distribution is only O-subexponential, the subexponential property almost holds. We also determine the exact tail behavior of the r-trimmed limits.

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Springer Science and Business Media LLC

Tập 30

1104-1129

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