International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 10, Pages 663-673

Stability of a characterization of normal distributions based on the first two conditional moments

Truc T. Nguyen1 and Khoan T. Dinh2

1Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403-0221, Ohio, USA
2Environmental Protection Agency, Washington 20460, DC, USA

Received 23 March 1998; Revised 27 July 1998

Copyright © 2000 Truc T. Nguyen and Khoan T. Dinh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A characterization of normal distributions of two independent random variables X and Y with a finite E[X2] based on the linearity of E[X|X+Y] and the homoscedasticity of var[X|X+Y] given by Rao (1976) is proved to be stable.