On Normal Variance-Mean Mixtures

Details On Normal Variance-Mean Mixtures On Normal Variance-Mean Mixtures

2011-06-12

arxiv.org/abs/1106.2333v1

Mathematics

Statistics Theory

Scientific paper

Normal variance-mean mixtures encompass a large family of useful distributions such as the generalized hyperbolic distribution, which itself includes the Student t, Laplace, hyperbolic, normal inverse Gaussian, and variance gamma distributions as special cases. We study shape properties of normal variance-mean mixtures, in both the univariate and multivariate cases, and determine conditions for unimodality and log-concavity of the density functions. This leads to a short proof of the unimodality of all generalized hyperbolic densities. We also interpret such results in practical terms and discuss discrete analogues.

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