论文标题
某些改进的高斯相关性不平等，对对称n晶格扩展到某些多元伽马分布，并且一些进一步的概率不平等现象
Some improved Gaussian correlation inequalities for symmetrical n-rectangles extended to some multivariate gamma distributions and some further probability inequalities
论文作者
论文摘要
如果绝对成分具有MTP2（MTP2完全正面的多变量2），则对对称N矩形的高斯相关性不平等（GCI）将得到改善。此处给定的类型的不平等至少对R^n或（0，Infinity）^n的所有MTP2-CDF持有，无处不在光滑。特别是，至少某些具有任何积极的实际“自由程度”的多元可分割的卡方分布函数（krishnamoorthy和parthasarathy的意义上的伽马分布）被证明是MTP2。此外，得出了一类多类多变量伽马分布的进一步可计算的概率不平等，并且对GCI型的不平等和类似类型的不等式的改进有所不同，具有三个组件，而不是两组组件 - 具有更特殊的相关结构。这些不等式背后的主要思想是找到具有正相关的给定相关矩阵的进一步相关矩阵，其相关矩阵与较小的相关性矩阵的相关性是m-matrix，而相应的多变量伽马分布函数在数值上可用。
The Gaussian correlation inequality (GCI) for symmetrical n-rectangles is improved if the absolute components have a joint cumulative distribution (cdf) which is MTP2 (multivariate totally positive of order 2). Inequalities of the here given type hold at least for all MTP2-cdfs on R^n or (0,infinity)^n with everywhere positive smooth densities. In particular, at least some infinitely divisible multivariate chi-square distribution functions (gamma distributions in the sense of Krishnamoorthy and Parthasarathy) with any positive real "degree of freedom" are shown to be MTP2. Moreover, further numerically calculable probability inequalities for a broad class of multivariate gamma distributions are derived and a different improvement for inequalities of the GCI-type - and of a similar type with three instead of two groups of components - with more special correlation structures. The main idea behind these inequalities is to find for a given correlation matrix with positive correlations a further correlation matrix with smaller correlations whose inverse is an M-matrix and where the corresponding multivariate gamma distribution function is numerically available.
