How Broad is the Class of Normal Scale Mixtures?
How Broad is the Class of Normal Scale Mixtures?
We study the class of scale mixtures of normal distributions with mean zero. Given that the $\operatorname{cdf} F(x)$ of such a mixture is fixed at two points, say $F(x_1) = \alpha_1, F(x_2) = \alpha_2$, we answer the question of how widely $F(x_3)$ can vary at some third point $x_3$. A …