  In this paper, we use a new partial order, called the f-majorization order.
The new order includes as special cases the majorization , the reciprocal
majorization and the p-larger orders. We provide a comprehensive account of the
mathematical properties of the f-majorization order and give applications of
this order in the context of stochastic comparison for extreme order statistics
of independent samples following the Frechet distribution and scale model. We
discuss stochastic comparisons of series systems with independent heterogeneous
exponentiated scale components in terms of the usual stochastic order and the
hazard rate order. We also derive new result on the usual stochastic order for
the largest order statistics of samples having exponentiated scale marginals
and Archimedean copula structure.
