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Minimally informative distributions with given rank correlation for use in uncertainty analysis. (English) Zbl 0873.62006

Summary: Minimum information bivariate distributions with uniform marginals and a specified rank correlation are studied. 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 convergence) for determining the minimum information distributions.

MSC:

62B10 Statistical aspects of information-theoretic topics
65C05 Monte Carlo methods
62H10 Multivariate distribution of statistics
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