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

Abstract

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.

Keywords

• Conditional density function
• normal close
• characteristic function
• small parameter..