Mathematical Sciences: Inequalities in Multivariate Analysisand Reliability

数学科学：多元分析和可靠性中的不等式

• 批准号: 8801327
• 负责人: Yung Tong
• 金额: $ 5.67万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801327&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Inequalities; Multivariate; Analysisand

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.

首席研究员将继续他的工作， 多元分析与可靠性中的概率不等式 理论 随机变量的具体依赖性质是 通过对数凹或舒尔凹等条件描述 密度、正相关性和排列增加 功能协调发展的 概率不等式是根据 随机变量和或序的性质 统计 例如，它将表明，舒尔凹 随机变量的密度导致Schur。凹密度的 部分和 正相关假设 可交换的随机变量导致更分散的顺序 统计数据，因此方差更大。 结果比较 随机变量的有序排列在 可靠性理论用于寻找系统的最佳组合。