On the Likelihood Ratio Test for Compound Distributions for Homogeneity of Mixing Proportions

We consider the problem of comparing two multivariate compound distributions each with component densities f ₁, (x) and f ₂(x) and with mixing proportions p _x and (1 – p_x) for the first compound distribution and p_y and (1 – p_y ) for the second. The likelihood ratio test of the hypothesis H ₀: p_x = p_y is presented by using the EM algorithm to derive the maximum likelihood estimates. This test is applied to some actual data under the assumption that the underlying component densities are normal. The result is contrasted with results obtained using some existing univariate methods of testing H₀.