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

这项研究涉及到与凸性有关的不平等和统计学中的正相关性。统计学的相关领域包括多元分析、可靠性理论、多重决策问题和统计计算。所使用的数学工具有凸性、优化论、条件化和混合分布。这项研究将通过多元优选法提供随机变量之间正相关性的偏序。探讨正相依在系统可靠性理论中的作用。将研究最优分配不等式中的公开问题，并通过正相关性进行统计实验的比较。

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.