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.
