  In this paper, we consider finite mixture models with modified proportional
hazard rates. Sufficient conditions for the usual stochastic order and the
hazard order are established under chain majorization. We study stochastic
comparisons under different settings of T-transform for various values of chain
majorization. We establish usual stochastic order and hazard rate order between
two mixture random variables when a matrix of model parameters and mixing
proportions changes to another matrix in some mathematical sense. Sufficient
conditions for the star order and Lorenz order are established under weakly
supermajorization. The results of this paper are illustrated with numerical
examples.
