标题： 关于正态方差-均值混合物 显示英文标题

标题： On Normal Variance-Mean Mixtures

摘要： 正态方差-均值混合分布包含大量有用的分布，例如广义双曲分布，而后者自身包括学生 t 分布、Laplace 分布、双曲分布、正态逆高斯分布和变异伽马分布等特例。 我们研究了正态方差-均值混合分布的形状性质，在单变量和多变量情况下确定了密度函数的单峰性和对数凹性的条件。 这为所有广义双曲密度函数的单峰性提供了简短证明。 我们也以实际意义来解读这些结果，并讨论离散版本的情况。 显示英文摘要

摘要： 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.