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

A new notion of majorization with applications to the comparison of extreme order statistics