Considers a problem in the estimation of linkages in genetics. McLachlan and Krishnan (1997) also discuss this problem and we present their model. For our purposes, it can be described as a multinomial model with the four categories C1, C2, C3, and C4. For a sample of size n, let X = (X1, X2, X3, X4) ′ denote the observed frequencies of the four categories. Hence, n = + 4 i=1 Xi. The probability model is