条件分布的MTP₂性质
An MTP$_2$ property for conditional distributions
浏览论文内容
中文总结 AI 辅助
研究引入条件分布的二阶多元全正性（cMTP₂）这一新正相关概念，验证其在多种分布和copula族中的性质及稳定性，进而得出马尔可夫结构定向依赖度量的比较结果。
中文摘要 AI 辅助
我们引入了一种新的正相关概念，即条件分布的二阶多元全正性，记为cMTP₂，它明确纳入了条件变量。该性质比密度的二阶多元全正性弱，但比分布函数、随机单调性和尾部单调性的二阶多元全正性强。它为连接这些经典正相关概念提供了自然的中间概念。我们验证了几种分布和copula族的cMTP₂性质，包括阿基米德copulas，并建立了马尔可夫积变换下的稳定性。由此得出马尔可夫结构产生的定向依赖度量的比较结果，包括Chatterjee的秩相关和相关的敏感性度量。
英文摘要
We introduce a new notion of positive dependence, namely multivariate total positivity of order two for conditional distributions, denoted cMTP$_2$, that explicitly incorporates the conditioning variables. This property is weaker than multivariate total positivity of order two for densities, but stronger than multivariate total positivity of order two for distribution functions, stochastic monotonicity, and tail monotonicity. It thus provides a natural intermediate concept linking these classical notions of positive dependence. We verify the cMTP$_2$ property for several distributions and copula families, including Archimedean copulas, and establish stability under Markov product transformations. As a consequence, we derive comparison results for measures of directed dependence arising from Markov structures, including Chatterjee's rank correlation and a related sensitivity measure.
