Open Access
December, 1959 Scale Mixing of Symmetric Distributions with Zero Means
E. M. L. Beale, C. L. Mallows
Ann. Math. Statist. 30(4): 1145-1151 (December, 1959). DOI: 10.1214/aoms/1177706099


Suppose that a distribution $A$ is a mixture of distributions similar to $B$ but with different scale parameters; or (almost equivalently) that a distribution $F$ is a convolution of a given distribution $G$ with some other distribution. We derive conditions on (i) the moments of $A$ and $F$ and (ii) on the derivatives of $A$ and $F$; these conditions are necessary, but are not sufficient in general. The conditions (ii) are appropriate when $B$ (or $G$) is of Polya type 3.


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E. M. L. Beale. C. L. Mallows. "Scale Mixing of Symmetric Distributions with Zero Means." Ann. Math. Statist. 30 (4) 1145 - 1151, December, 1959.


Published: December, 1959
First available in Project Euclid: 27 April 2007

zbMATH: 0104.12001
MathSciNet: MR110130
Digital Object Identifier: 10.1214/aoms/1177706099

Rights: Copyright © 1959 Institute of Mathematical Statistics

Vol.30 • No. 4 • December, 1959
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