Abstract
A multivariate conditional joint probability distribution of a set of K normalized structure factors has been developed using a novel approach. The covariance matrix of the distribution is calculated for all the space groups in terms of linear combinations of specific unitary structure factors. It is shown that if any number of off-diagonal elements are set arbitrarily to zero, an approximation is obtained to the covariance matrix which corresponds to a particular set of a priori conditions. The importance of this result in practical phase-determining methods is pointed out. Group theory is used to obtain results valid for all space groups. The multivariate distribution is used to calculate more general versions of the Cochran and Woolfson sign probability and the Karle and Hauptman tangent formulae.
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