Mathematical Sciences: Inequalities in Multivariate Analysisand Reliability

首席研究员将继续研究多元分析和可靠性理论中的概率不等式。随机变量的特定依赖性质通过log等条件来描述。凹的或凹的。凹密度，正相关，排列递增函数。概率不等式是根据随机变量和或序统计量的性质推导出来的。例如，它将显示舒尔。随机变量的凹密度导致Schur。部分和的凹密度。可交换随机变量的正相关假设导致序统计量更分散，从而导致更大的方差。由此得到的随机变量的比较和顺序排列在可靠性理论中用于寻找系统的最优装配。

The principal investigator will continue his work on probability inequalities in multivariate analysis and reliability theory. Specific dependence properties of random variables are described via conditions such as log.concave or Schure.concave densities, positive dependence, and arrangement increasing functions. The probability inequalities are deduced in terms of properties of the sums of random variables or the order statistics. For example it will be shown that the Schur.concave density of random variables leads to Schur.concave density of the partial sums. The assumption of positive dependence for exchangeable random variables leads to more spread out order statistics and hence bigger variance. The resulting comparisons and order arrangements of random variables are useful in reliability theory for finding the optimal assembly of systems.