Given an OTS of length \(T\) with range \(\mathcal{S}=\{s_0, s_1, s_2, \ldots, s_n\}\) (\(s_0 < s_1 < s_2 < \ldots < s_n\)),
\(\overline{X}_t=\{\overline{X}_1,\ldots, \overline{X}_T\}\), the function computes the
estimated skewness given by \(\widehat{skew}_{d}=\sum_{i=0}^n\big(d(s_i,s_n)-d(s_i,s_0)\big)\widehat{p}_i\),
where \(d(\cdot, \cdot)\) is a distance between ordinal states and \(\widehat{p}_k\) is the standard estimate
of the marginal probability for state \(s_k\) computed from the realization \(\overline{X}_t\).