Anderson proved the existence of a link between
the parameters of the mixture Gaussian model and those
of corresponding logistic model. Links between the two
subpopulations can be obtained in a stochastic case where, the
variables vector x and x∗ defined over Ω and Ω∗ are Gaussian,
homoscedastic conditionally in the groups and the matrices of
common variance-covariance are noted in the following way