title: A characterization of the compound multiparameter hermite gamma distribution via Gauss's principle.
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.
authors.affiliation: Wolters Kluwer Financial Services, Seefeldstrasse 69, 8008 Zürich, Switzerland.
authors.forename: Werner
authors.initials: W
authors.lastname: Hürlimann
mesh_terms: D016013:Likelihood Functions; D015233:Models, Statistical; D016011:Normal Distribution; D016008:Statistical Distributions