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STABILITY OF A CHARACTERIZATION OF NORMAL DISTRIBUTIONS BASED ON THE FIRST TWO CONDITIONAL MOMENTS

摘要


A characterization of normal distributions of two independent random variables X and Y with a finite E[X^2] basedon the linearity of E[X | X + Y] andthe homoscedasticity of var[X | X+Y] given by Rao (1976) is provedto be stable.

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