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Characterizations of normal distributions and EDF goodness-of-fit tests

Authors:	Truc?T.?Nguyen author-information" > author-information__contact u-icon-before" > mailto:tnguyen@bgnet.bgsu.edu" title=" tnguyen@bgnet.bgsu.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Khoan?T.?Dinh author-information" > author-information__contact u-icon-before" > mailto:dinh.khoan@epamail.epa.gov" title=" dinh.khoan@epamail.epa.gov" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Department of Mathematics and Statistics, Bowling Green State University, OH 43403-0221 Bowling Green, USA;(2) US Environmental Protection Agency, US Environmental Protection Agency, DC 20460 Washington, USA

Abstract:	Two characterizations of a normal distribution with an unknown variance based on the corresponding UMVU estimators of the density functions are given, depending on whether its mean is known, or unknown. Applications of these characterization results in the procedures to construct empirical distribution function (EDF) goodness-of-fit tests for normal distributions are mentioned.Received April 2000/Revised April 2002

Keywords:	Conditional density function UMVUE of the density function Characteristic function
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