  Stochastic ordering among distributions has been considered in a variety of
scenarios. Economic studies often involve research about the ordering of
investment strategies or social welfare. However, as noted in the literature,
stochastic orderings are often a too strong assumption which is not supported
by the data even in cases in which the researcher tends to believe that a
certain variable is somehow smaller than other. Instead of considering this
rigid model of stochastic order we propose to look at a more flexible version
in which two distributions are said to satisfy an approximate stochastic order
relation if they are slightly contaminated versions of distributions which do
satisfy the stochastic ordering. The minimal level of contamination that makes
this approximate model hold can be used as a measure of the deviation of the
original distributions from the exact stochastic order model. Our approach is
based on the use of trimmings of probability measures. We discuss the
connection between them and the approximate stochastic order model and provide
theoretical support for its use in data analysis. We also provide simulation
results.
