TY - JOUR
T1 - Uniform designs for mixture-amount experiments and for mixture experiments under order restrictions
AU - Tian, Guoliang
AU - Fang, Kaitai
N1 - Funding Information:
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.
PY - 1999/5
Y1 - 1999/5
N2 - 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.
AB - 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.
KW - Discrepancy
KW - Isotonic restriction
KW - Monte Carlo optimization
KW - Multivariate distribution
KW - Uniform design
UR - http://www.scopus.com/inward/record.url?scp=0042233438&partnerID=8YFLogxK
U2 - 10.1007/BF02882241
DO - 10.1007/BF02882241
M3 - Article
AN - SCOPUS:0042233438
SN - 1006-9283
VL - 42
SP - 456
EP - 470
JO - Science in China, Series A: Mathematics, Physics, Astronomy
JF - Science in China, Series A: Mathematics, Physics, Astronomy
IS - 5
ER -