Distribution of likelihood ratio in relation to the exclusion probability

The relation between the exclusion probability (E) and the paternity probability is derived by assuming the distributions of logarithm of paternity likelihood ratio, log(Y/X) for true fathers and unexcluded non-fathers as the normal distributions. Under this assumption the value log(1-E) is equal to the mean of the mean value for true fathers (a) and that for unexcluded non-fathers (b), i.e., log(1-E)=(a+b)/2. This relation holds quite well for the various actual distributions of log(Y/X) of father-child combinations and those of father-mother-child combinations using 14 blood group systems. Therefore, the derived relation is found to be a convenient way to deduce one of the three quantities (E, a, b) from the remaining two quantities in the actual distributions.