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A characterization of the compound multiparameter hermite gamma distribution via Gauss's principle
1Wolters Kluwer Financial Services, Seefeldstrasse 69, 8008 Zürich, Switzerland.
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.
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