Convolution-invariant subclasses of generalized hyperbolic distributions

Krzysztof Podgórski and Jonas Wallin

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 1, 98-103

Abstract: It is rigorously shown that the generalized Laplace distributions and the normal inverse Gaussian distributions are the only subclasses of the generalized hyperbolic distributions that are closed under convolution. The result is obtained by showing that the corresponding two classes of variance mixing distributions—gamma and inverse Gaussian—are the only convolution-invariant classes of the generalized inverse Gaussian distributions.

Date: 2016
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DOI: 10.1080/03610926.2013.821489

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