论文标题
多元极端的随机排序
Stochastic ordering in multivariate extremes
论文作者
论文摘要
本文考虑了上部矫正剂的多元随机顺序，下骨和正象限依赖性（PQD）及其指数指标。仅当它适用于相应的指数度量时，它显示了它适用于最大稳定分布的每个顺序。该发现对于上部矫正剂（因此是PQD阶）是不平凡的。从尺寸$ d \ geq 3 $这三个订单不等式，可能会发生多种现象。但是，每个简单的最大稳定分布pqd都会以相应的独立模型为主导，并由完全依赖的模型主导PQD。在参数模型中，根据其参数空间内的自然顺序，不对称的Dirichlet家族和Hüsler-Reiss家族被证明是PQD订购的。对于Hüsler-Reiss家族而言，这即使对于超模型秩序也是如此。
The article considers the multivariate stochastic orders of upper orthants, lower orthants and positive quadrant dependence (PQD) among simple max-stable distributions and their exponent measures. It is shown for each order that it holds for the max-stable distribution if and only if it holds for the corresponding exponent measure. The finding is non-trivial for upper orthants (and hence PQD order). From dimension $d\geq 3$ these three orders are not equivalent and a variety of phenomena can occur. However, every simple max-stable distribution PQD-dominates the corresponding independent model and is PQD-dominated by the fully dependent model. Among parametric models the asymmetric Dirichlet family and the Hüsler-Reiss family turn out to be PQD-ordered according to the natural order within their parameter spaces. For the Hüsler-Reiss family this holds true even for the supermodular order.
