Determination of joint distributions from marginal distributions in dichotomous systems

In many areas of research in which the experimenter deals with a set of dichotomous dimensions it is often desirable to specify them in terms of marginal distributions and some conditional distributions. This paper develops a set of systematic procedures for determination of joint distributions with an arbitrary number of dimensions. Most of these procedures require only addition and/or subtraction. An extension of the procedures permits easy determination of covariance and correlation matrices.This research was supported in part by National Institutes of Health grant No. MH-12541. Part of this work was done at Stanford University during work sessions of the 1967 Summer Conference on Mathematical Models in Perception and Learning. The author is indebted to Richard S. Bogartz for many helpful comments.