Abstract
With order statistics of the uniform distribution on [0, l], 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.
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This work was partially supported by a Hong Kong UGC-RGC grant, the Statistics Research and Consultancy Centre of HK-BU, and the Chinese Academy of Sciences.
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Tian, G., Fang, K. Uniform designs for mixture-amount experiments and for mixture experiments under order restrictions. Sci. China Ser. A-Math. 42, 456–470 (1999). https://doi.org/10.1007/BF02882241
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DOI: https://doi.org/10.1007/BF02882241