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Characterization of the p-generalized normal distribution

https://doi.org/10.1016/j.jmva.2008.07.006Get rights and content
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Abstract

It is a well known fact that invariance under the orthogonal group and marginal independence uniquely characterizes the isotropic normal distribution. Here, a similar characterization is provided for the more general class of differentiable bounded Lp-spherically symmetric distributions: Every factorial distribution in this class is necessarily p-generalized normal.

AMS subject classification

62E10

Keywords

Characterization
Generalized normal distribution
Exponential power distribution
Lp-spherically symmetric distributions

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