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September, 1978 How Broad is the Class of Normal Scale Mixtures?
Bradley Efron, Richard A. Olshen
Ann. Statist. 6(5): 1159-1164 (September, 1978). DOI: 10.1214/aos/1176344318

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.

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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

Information

Published: September, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0385.62013
MathSciNet: MR501500
Digital Object Identifier: 10.1214/aos/1176344318

Subjects:
Primary: 62E10
Secondary: 62G05

Keywords: normal scale mixtures , Tchebycheff systems

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 5 • September, 1978
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