  In the literature, quite a few measures have been proposed for quantifying
the deviation of a probability distribution from symmetry. The most popular of
these skewness measures are based on the third centralized moment and on
quantiles. However, there are major drawbacks in using these quantities. These
include a strong emphasis on the distributional tails and a poor asymptotic
behaviour for the (empirical) moment based measure as well as difficult
statistical inference and strange behaviour for discrete distributions for
quantile based measures.
  Therefore, in this paper, we introduce skewness measures based on or
connected with expectiles. Since expectiles can be seen as smoothed versions of
quantiles, they preserve the advantages over the moment based measure while not
exhibiting most of the disadvantages of quantile based measures. We introduce
corresponding empirical counterparts and derive asymptotic properties. Finally,
we conduct a simulation study, comparing the newly introduced measures with
established ones, and evaluating the performance of the respective estimators.
