Abstract
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 brief final section mentions extensions of our theorem.
Citation
Bradley Efron. Richard A. Olshen. "How Broad is the Class of Normal Scale Mixtures?." Ann. Statist. 6 (5) 1159 - 1164, September, 1978. https://doi.org/10.1214/aos/1176344318
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