In the joint SA training algorithm <cite>[4]</cite> , we define another form of mixture distribution as follows: where ζ = {ζ1, . . . , ζm} with ζ1 = 0 and ζ l is the hypothesized value of the log ratio of Z l (λ) with respect to Z1(λ), namely log . Z1(λ) is chosen as the reference value and can be calculated exactly.