Recently, Bartoszewicz [5,6] considered mixtures of exponential
distributions treated as the Laplace transforms of mixing distributions
and established some stochastic order relations between them: star order,
dispersive order, dilation. In this article the preservation of the
likelihood ratio, hazard rate, reversed hazard rate, mean residual life,
and excess wealth orders under exponential mixtures is studied. Some new
preservation results for the dispersive order are given, as well as the
preservation of the convex transform order, and the star one is
discussed.