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The Scientific World Journal
Volume 2013, Article ID 468418, 7 pages
http://dx.doi.org/10.1155/2013/468418
Research Article

A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s Principle

Wolters Kluwer Financial Services, Seefeldstrasse 69, 8008 Zürich, Switzerland

Received 13 August 2013; Accepted 22 September 2013

Academic Editors: N. Marwan, J. Pacheco, and S. Umarov

Copyright © 2013 Werner Hürlimann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the class of those distributions that satisfy Gauss's principle (the maximum likelihood estimator of the mean is the sample mean) and have a parameter orthogonal to the mean. It is shown that this so-called “mean orthogonal class” is closed under convolution. A previous characterization of the compound gamma characterization of random sums is revisited and clarified. A new characterization of the compound distribution with multiparameter Hermite count distribution and gamma severity distribution is obtained.