  In some inferential statistical methods, such as tests and confidence
intervals, it is important to describe the stochastic behavior of statistical
functionals, aside from their large sample properties. We study such behavior
in terms of the usual stochastic order. For this purpose, we introduce a
generalized family of stochastic orders, which is referred to as transform
orders, showing that it provides a flexible framework for deriving stochastic
monotonicity results. Given that our general definition makes it possible to
obtain some well-known ordering relations as particular cases, we can easily
apply our method to different families of functionals. These include some
prominent inequality measures, such as the generalized entropy, the Gini index,
and its generalizations. We also illustrate the applicability of our approach
by determining the least favorable distribution, and the behavior of some
bootstrap statistics, in some goodness-of-fit testing procedures.
