Minimally informative distributions with given rank correlation for use in uncertainty analysis
- 1 April 1997
- journal article
- research article
- Published by Taylor & Francis in Journal of Statistical Computation and Simulation
- Vol. 57 (1-4) , 143-174
- https://doi.org/10.1080/00949659708811806
Abstract
Minimum information bivariate distributions with uniform marginals and a specified rank correlation are studied in this paper. These distributions play an important role in a particular way of modeling dependent random variables which has been used in the computer code UNICORN for carrying out uncertainty analyses. It is shown that these minimum information distributions have a particular form which makes simulation of conditional distributions very simple. Approximations to the continuous distributions are discussed and explicit formulae are determined. Finally a relation is discussed to DAD theorems, and a numerical algorithm is given (which has geometric rate of covergence) for determining the minimum information distributions.Keywords
This publication has 10 references indexed in Scilit:
- Entropy and equilibrium states in classical statistical mechanicsPublished by Springer Nature ,2007
- Entropy Minimization, DAD Problems, and Doubly Stochastic KernelsJournal of Functional Analysis, 1994
- On the optimal entropy analysisEuropean Journal of Operational Research, 1992
- Decomposition of Multivariate FunctionsCanadian Journal of Mathematics, 1992
- Hilbert’s projective metric and iterated nonlinear mapsMemoirs of the American Mathematical Society, 1988
- Monte Carlo Sampling for Generalized Knowledge Dependence with Application to Human ReliabilityRisk Analysis, 1986
- Fortran 77 program and user's guide for the generation of Latin hypercube and random samples for use with computer modelsPublished by Office of Scientific and Technical Information (OSTI) ,1984
- $I$-Divergence Geometry of Probability Distributions and Minimization ProblemsThe Annals of Probability, 1975
- On a Theorem of P. NowosadJournal of Mathematical Analysis and Applications, 1967
- On the integral equation κf = 1f arising in a problem in communicationJournal of Mathematical Analysis and Applications, 1966