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Convolution-invariant subclasses of generalized hyperbolic distributions

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  • Krzysztof Podgórski
  • Jonas Wallin

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.

Suggested Citation

  • Krzysztof Podgórski & Jonas Wallin, 2016. "Convolution-invariant subclasses of generalized hyperbolic distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(1), pages 98-103, January.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:1:p:98-103
    DOI: 10.1080/03610926.2013.821489
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    Cited by:

    1. Janine Balter & Alexander J. McNeil, 2018. "On the Basel Liquidity Formula for Elliptical Distributions," Risks, MDPI, vol. 6(3), pages 1-13, September.

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