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

István Berkes; László Györfi; Péter Kevei

doi:10.1007/s10959-016-0677-5

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

István Berkes, László Györfi, Péter Kevei^*

^*Corresponding author for this work

Institute of Statistics (5060)

Research output: Contribution to journal › Article › peer-review

Abstract

We provide exact asymptotics for the tail probabilities P{S_n,r>x} as x → ∞, 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.

Original language	English
Pages (from-to)	1104-1129
Number of pages	26
Journal	Journal of Theoretical Probability
Volume	30
Issue number	3
DOIs	https://doi.org/10.1007/s10959-016-0677-5
Publication status	Published - 15 Mar 2016

Keywords

Semistable law
St. Petersburg sum
Tail asymptotic
Trimmed sum

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

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tail_probabilities_of_st_petersburg_sums_trimmed_sums_and_their_limitSubmitted manuscript, 153 KBLicence: CC BY 4.0

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AU - Kevei, Péter

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AB - We provide exact asymptotics for the tail probabilities P{Sn,r>x} as x → ∞, for fixed n, where Sn,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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Tail Probabilities of St. Petersburg Sums, Trimmed Sums, and Their Limit

Abstract

Keywords

ASJC Scopus subject areas

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