With order statistics of the uniform distribution on [0, 1], exponential and beta distributions, a stochastic representation is obtained for the uniform distribution over various domains, where A-type domains are clos...With order statistics of the uniform distribution on [0, 1], exponential and beta distributions, a stochastic representation is obtained for the uniform distribution over various domains, where A-type domains are closely associated with reliability growth analysis, order restricted statistical inference and isotonic regression theory, V-type domains are connected with the mixture-amount experiments, and T-type domains are well related to mixture experiments. With these stochastic representations, the corresponding uniform distribution and number-theoretic nets can be generated. This approach seems to be new and is called order statistics method. Some examples on reliability growth analysis and experimental design are presented.展开更多
基金This work was Partially supported by a Hong Kong UGC-RGC grantthe statitics Research and Consultancy Centre of HK-BUthe Chinese Academy of Sciences
文摘With order statistics of the uniform distribution on [0, 1], exponential and beta distributions, a stochastic representation is obtained for the uniform distribution over various domains, where A-type domains are closely associated with reliability growth analysis, order restricted statistical inference and isotonic regression theory, V-type domains are connected with the mixture-amount experiments, and T-type domains are well related to mixture experiments. With these stochastic representations, the corresponding uniform distribution and number-theoretic nets can be generated. This approach seems to be new and is called order statistics method. Some examples on reliability growth analysis and experimental design are presented.
