We extend the construction principle of multivariate phase-type distributions to establish an analytically tractable class of heavy-tailed multivariate random variables whose marginal distributions are of Mittag–Leffler type with arbitrary index of regular variation. The construction can essentially be seen as allowing a scalar parameter to become matrix-valued. The class of distributions is shown to be dense among all multivariate positive random variables and hence provides a versatile candidate for the modelling of heavy-tailed, but tail-independent, risks in various fields of application.

中文翻译：

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多元矩阵 Mittag-Leffler 分布

我们扩展了多元相类型分布的构造原理，以建立一个分析上易于处理的重尾多元随机变量类，其边缘分布是具有任意规则变化指数的 Mittag-Leffler 类型。该构造本质上可以被视为允许标量参数变为矩阵值。分布类别在所有多元正随机变量中显示为密集的，因此为各种应用领域中的重尾但与尾无关的风险建模提供了一个通用的候选者。