  In this work we show how coupling and stochastic dominance methods can be
successfully applied to a classical problem of rigorizing Pearson's skewness.
Here, we use Fr\'{e}chet means to define generalized notions of positive and
negative skewness that we call truly positive and truly negative. Then, we
apply stochastic dominance approach in establishing criteria for determining
whether a continuous random variable is truly positively skewed. Intuitively,
this means that scaled right tail of the probability density function exhibits
strict stochastic dominance over equivalently scaled left tail. Finally, we use
the stochastic dominance criteria and establish some basic examples of true
positive skewness, thus demonstrating how the approach works in general.
