Scale Mixing of Symmetric Distributions with Zero Means
Beale, E. M. L. ; Mallows, C. L.
Ann. Math. Statist., Tome 30 (1959) no. 4, p. 1145-1151 / Harvested from Project Euclid
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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.
Publié le : 1959-12-14
Classification:  
@article{1177706099,
     author = {Beale, E. M. L. and Mallows, C. L.},
     title = {Scale Mixing of Symmetric Distributions with Zero Means},
     journal = {Ann. Math. Statist.},
     volume = {30},
     number = {4},
     year = {1959},
     pages = { 1145-1151},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177706099}
}

Beale, E. M. L.; Mallows, C. L. Scale Mixing of Symmetric Distributions with Zero Means. Ann. Math. Statist., Tome 30 (1959) no. 4, pp.  1145-1151. http://gdmltest.u-ga.fr/item/1177706099/