Mathematical Sciences: Convexity-Related Inequalities and Positive Dependence in Statistics

数学科学：统计学中与凸性相关的不等式和正相关性

• 批准号: 9001721
• 负责人: Yung Tong
• 金额: $ 7.59万
• 依托单位: Georgia Tech Research Corporation - GA Tech Research Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001721&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Convexity; Related; Inequalities

This research involves convexity-related inequalities and positive dependence in statistics. The related areas in statistics include multivariate analysis, reliability theory, multiple decision problems, and statistical computing. The mathematical tools to be used are convexity, majorization theory, conditioning and mixture of distributions. The research will provide a partial ordering of positive dependence among random variables via multivariate majorization. The effects of positive dependence in system reliability theory will be explored. Open problems in optimal-partitioning inequalities will be studied and a comparison of statistical experiments via positive dependence will be made.

这项研究涉及凸相关的不等式和 统计学上的正相关。 中的相关领域 统计学包括多变量分析，可靠性理论， 多决策问题和统计计算。的 要使用的数学工具是凸性，优化理论， 条件和混合分布。这项研究将 提供随机变量之间正相关的偏序 变量通过多变量优化。积极的影响 将探讨系统可靠性理论中的相关性。开放 将研究最优划分不等式中的问题 并通过积极的统计实验比较 将产生依赖性。