Minimally informative distributions with given rank correlation for use in uncertainty analysis

References

• Bedford T. Cooke R. Reliability Methods as management tools: dependence modelling and partial mission success 1995 Proceedings ESREL'95
   Google Scholar
• Borwein , J.M. and Lewis , A.S. 1992 . Decomposition of multivariate functions . Can. J. Math , 44 : 463
   Web of Science ®Google Scholar
• Borwein , J.M. , Lewis , A.S. and Nussbaum , R.D. 1994 . Entropy minimization, DAD problems, and doubly stochastic kernels . Journal of Functional Analysis , 123 : 264
   Web of Science ®Google Scholar
• Cooke , R. and Waij , R. 1986 . Monte Carlo Sampling for generalized knowledge dependence with application to human reliability . Risk Analysis , 6 ( 3 ) : 335
   PubMed Web of Science ®Google Scholar
• Cooke , R.M. 1995 . UNICORN: Methods and code for uncertianty analysis , Warrington, , UK : AEA Tenchnologies .
   Google Scholar
• Csiszar , I. 1975 . I-divergence geometry of probability distributions and minimization problems . Annals of Probability , 3 : 146
   Web of Science ®Google Scholar
• van Dorp , J.R. December 1991 . Dependence Modeling for Uncertainty Analysis , December , The Netherlands : Delft University of Technology .
   Google Scholar
• Guiasu , S. 1977 . Information Theory with Applications , New York : McGraw-Hill .
   Google Scholar
• Hutchinson , T.P. and Lai , C.D. 1990 . Continuous Bivariate Distributions, Emphasizing Applications , Adelaide, , Australia : Rumsby Scientific Publishing . 5000
   Google Scholar
• Iman , R.L. and Conover , W.J. 1982 . A distribution free approach to inducing rank correlations among input variables . Commun. Stat. Sim. Computa , 11 ( 3 ) : 331
   Google Scholar
• Iman R. L. Shortencarrier M. J. A FORTRAN 77 program and users guide for the generation of the Latin hypercube and random sampling foruse with computer models 1984 NUREG/CR-3624
   Google Scholar
• Johnson , M.E. and Ramberg , J.S. 1977 . Transformations of the multivariate normal distribution with application to simulation , Los Alamos, New Mexico : Scientific Laboratory . Technical report, LAUR-77-2595
   Google Scholar
• Karlin , S. 1968 . Total Positivity , California : Standford University Press Stanford .
   Google Scholar
• Karlin , S. and Nirenberg , L. 1967 . On a theorem of P. Nowosad . J. Math. Anal. Appl , 17 : 61
   Web of Science ®Google Scholar
• Kullback , S. 1959 . Information Theory and Statistics , Wiley .
   Google Scholar
• Oscar , E. 1973 . Entropy and Equilibrium States in Classical Statistical Mechanics Statistical Mechanics & Mathematical Problems . Springer Lecture Notes in Physics , 20 : 1
   Google Scholar
• Marshall , A.W. and Olkin , I. 1979 . Inequalities: Theory of Majorization and Its Application , Edited by: Bellman , Richard. Vol. 143 , London, New York : Academic Press . in Mathematics in Science and Engineering
   Google Scholar
• Meeuwissen , A.M.H. Novermber 1993 . Dependent Random Variables in Uncertainty Analysis , Novermber , Delft, , The Netherlands : Ph.D. Thesis Delft University of Technology .
   Google Scholar
• Meeuwissen , A.M.H. and Cooke , R.M. 1994 . Tree dependent random variables , Delft University of Technology . Report 94-28 TWI
   Google Scholar
• Nowosad , P. 1966 . On the integral equation K f = 1/f arising in a problem in communication . J. Math. Anal. Appl , 14 : 484
   Web of Science ®Google Scholar
• Nussbaum , R.D. 1988 . Hilbert’s projective metric and iterated non-linear maps . Memoirs of the Amer. Math. Soc , 75 ( 391 )
   Web of Science ®Google Scholar
• Nussbaum , R.D. 1989 . Hilbert’s projective metric and iterated non-linear maps, II, Memoirs of the Amer . Math. Soc , 79 ( 401 )
   Web of Science ®Google Scholar
• de Ruyter J. Uncertainty Analysis: An evaluation of methods, techniques and codes 1994 ECN-NT-RA-94-09
   Google Scholar
• Tsao , H.S.J. , Fang , S.C. and Lee , D.N. 1992 . On the Optimal Entropy Analysis . European J. of Op Res , 59 ( 401 ) : 324 – 329 .
   Google Scholar
• Tong Y. L. The Gaussian Distribution 1990
   Google Scholar
• Uffink , J.B.M. 1990 . Measures of Uncertainty and the Uncertainty Principle The Netherlands PhD Thesis, Rijksuniversiteit Utrecht
   Google Scholar
• Zwart , R. 1992 . Approximating maximum entropy distribution by diagonal band distribution TU Delft Unpublished report
   Google Scholar