Other formats:
BibTeX
LaTeX
RIS
@inproceedings{755096,
author = {Horová, Ivanka and Koláček, Jan and Zelinka, Jiří and ElandShaarawi, Abdel H.},
address = {Mexico},
booktitle = {Advanced topics on mathematical biology and ecology},
edition = {1},
keywords = {cumulative distribution function; kernel smoothing; reflection method},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Mexico},
isbn = {978-960-6766-32-9},
pages = {122-127},
publisher = {WSEAS Press},
title = {Smooth Estimates of Distribution Functions with Application in Environmental Studies},
year = {2008}
}
TY - JOUR
ID - 755096
AU - Horová, Ivanka - Koláček, Jan - Zelinka, Jiří - El-Shaarawi, Abdel H.
PY - 2008
TI - Smooth Estimates of Distribution Functions with Application in Environmental Studies
PB - WSEAS Press
CY - Mexico
SN - 9789606766329
KW - cumulative distribution function
KW - kernel smoothing
KW - reflection method
N2 - The most commonly used nonparametric estimate of a cumulative distribution function F is an empirical distribution function F_n. But F_n is a step function even in case that F is continuous. The present paper aims to provide a smooth estimate of F. Kernel methods seem to be adequate for this purpose. There exist several methods how to choose a bandwidth. We propose a method of bandwidth selection based on a suitable estimate of Mean Integrated Square Error. We also focus on an estimate of a cumulative distribution function in case that random variables X_1,...,X_n are nonnegative. The aforementioned methods are not reliable near the point x=0. In order to avoid this problem we propose a~reflection method. A simulation study is conducted to compare the performance of the different methods of bandwidth choice. Theoretical results are applied to the data concerning the content of toxic material in the fish population in Lake Ontario.
ER -
HOROVÁ, Ivanka, Jan KOLÁČEK, Jiří ZELINKA and Abdel H. EL-SHAARAWI. Smooth Estimates of Distribution Functions with Application in Environmental Studies. In \textit{Advanced topics on mathematical biology and ecology}. 1st ed. Mexico: WSEAS Press, 2008, p.~122-127. ISBN~978-960-6766-32-9.
|
