It is a consequence of the minimum discrimination information theorem, that minimum discrimination information distributions are formulated as members of an exponential family (CAMPBELL, 1970; KULLBACK, 1959). For applications to the analysis of contingency tables i t is useful to express the exponential family as a log-linear additive model (Ku, VARNER, KULLBACK, 1971; KULLBACK, 1970 b j. We propose to illustrate in terms of a particular set of data the relations implied by hypotheses and subhypotheses of interest on the values of the natural parameters and random variables of the exponential family, the related moment parameters, and the estimates of the cell entries.
Since our estimates in this discussion are constrained to satisfy certain linear relations based on observed values, the minimum discrimination information estimates are maximum likelihood estimates and the associated minimum discrimination information statistics are log-likelihood ratio statistics (CAMPBELL, 1970; DARROCH, RATCLIFF, 1972; KULLBACK, 1970 a, b). Further references to the literature on the log-linear model map be found in papers by BISHOP (1971), DEMPSTER (1971), GOKHALE (1971), Ku et a. (1971), PLACKETT (1969).
Table 1 Data on number of mothers with previous infant losses (COCHRAN, 1954) S o . of mothers with j = 1 j = 2 k i Losses No losses 1 1 Problems 20 82 2 Controls 10 54 Birth 2 1 Problems 26 41 order 2 Controls 16 30 3 1 Problems 27 22 2 Controls 14 23
The particular data we shall use were first presented by COCHRAN (1954), are given in table 1, and have been examined from various points of view (BERK-25*