Open Access
Translator Disclaimer
December, 1971 On Moments of Infinitely Divisible Distribution Functions
Stephen James Wolfe
Ann. Math. Statist. 42(6): 2036-2043 (December, 1971). DOI: 10.1214/aoms/1177693071

Abstract

Let $F(x)$ be an infinitely divisible distribution function with a Levy-Khintchine function $G(u)$ and let $p$ be any positive number. It is shown that $F(x)$ has an absolute moment of the $p$th order if and only if $G(u)$ has an absolute moment of the $p$th order, and $F(x)$ has an exponential moment of the $p$th order if and only if $G(u)$ has an exponential moment of the $p$th order. This result generalizes a theorem of J. M. Shapiro. Other related results are also obtained.

Citation

Download Citation

Stephen James Wolfe. "On Moments of Infinitely Divisible Distribution Functions." Ann. Math. Statist. 42 (6) 2036 - 2043, December, 1971. https://doi.org/10.1214/aoms/1177693071

Information

Published: December, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0227.60012
MathSciNet: MR300319
Digital Object Identifier: 10.1214/aoms/1177693071

Rights: Copyright © 1971 Institute of Mathematical Statistics

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.42 • No. 6 • December, 1971
Back to Top