The Annals of Mathematical Statistics

Error Estimates for the Weak Convergence to Certain Infinitely Divisible Laws

Thomas A. Hern

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Abstract

Let $F_n$ denote the distribution function of the $n$th row sum of a triangular array of infinitesimal, rowwise independent random variables, and let $F^\ast$ denote the limiting infinitely divisible distribution function. Bounds are obtained for $\sup_{-\infty < x < \infty} |F_n(x) - F^\ast(x)|$ in the case that the means are finite and also for the attraction to a stable law with exponent $\alpha \leqq 1$. Conditions for convergence of these bounds are given.

Article information

Source
Ann. Math. Statist., Volume 43, Number 5 (1972), 1592-1602.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692391

Digital Object Identifier
doi:10.1214/aoms/1177692391

Mathematical Reviews number (MathSciNet)
MR343346

Zentralblatt MATH identifier
0249.60011

JSTOR
links.jstor.org

Citation

Hern, Thomas A. Error Estimates for the Weak Convergence to Certain Infinitely Divisible Laws. Ann. Math. Statist. 43 (1972), no. 5, 1592--1602. doi:10.1214/aoms/1177692391. https://projecteuclid.org/euclid.aoms/1177692391


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