@book{4c7ced2dbb084ba584dbad19667f41a6,
title = "Tail behavior of the empirical distribution function of convolutions",
abstract = "Control charts based on convolutions require study of the tail behavior of the empirical distribution function of convolutions. It is well-known that this empirical distribution function at a fixed argument $x$ is asymptotically normal. The asymptotic normality is extended here to sequences $x_{n}$ tending to infinity at a suitable rate. At still larger $x_{n}$'s Poisson limiting distributions come in for the classical empirical distribution function. Surprisingly, this property does not generalize to its convolution counterpart, since for those $x_{n}$'s it is degenerate at $0$ with probability tending to 1. Exact inequalities for the tail behavior are presented as well.",
keywords = "MSC-62E20, EWI-3560, IR-65924, MSC-62P30, METIS-219690, MSC-62G30",
author = "Willem/Wim Albers and W.C.M. Kallenberg",
note = "Imported from MEMORANDA",
year = "2004",
language = "Undefined",
series = "Memorandum Faculty of Applied Mathematics",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1740",
}