论文标题
$ \ ell_p $ -norm对称生存功能的随机分解功能
Stochastic decomposition for $\ell_p$-norm symmetric survival functions on the positive orthant
论文作者
论文摘要
我们得出了一个随机表示，用于正偏$（0，\ infty）^d $上概率分布的随机表示，其组件之间的关联在所有概率定律中与$ \ ell_p $ - norm对称生存函数之间的关联至少。它是通过标准单元上的均匀分布的转换给出的，该分布乘以某些Beta分布的独立有限混合物和统一的附加原子。一方面，这意味着具有$ \ ell_p $ -norm对称生存函数的任意概率定律的有效仿真算法。另一方面，该结果被利用以构建一种精确的模拟算法，以无限地划分的最大可划分概率分布，其指数度量具有$ \ ell_p $ -Norm对称生存函数。这两个应用程序都将案例$ p = 1 $的现有结果概括为任意$ p \ geq 1 $的情况。
We derive a stochastic representation for the probability distribution on the positive orthant $(0,\infty)^d$ whose association between components is minimal among all probability laws with $\ell_p$-norm symmetric survival functions. It is given by a transformation of a uniform distribution on the standard unit simplex that is multiplied with an independent finite mixture of certain beta distributions and an additional atom at unity. On the one hand, this implies an efficient simulation algorithm for arbitrary probability laws with $\ell_p$-norm symmetric survival function. On the other hand, this result is leveraged to construct an exact simulation algorithm for max-infinitely divisible probability distributions on the positive orthant whose exponent measure has $\ell_p$-norm symmetric survival function. Both applications generalize existing results for the case $p=1$ to the case of arbitrary $p \geq 1$.
