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 asymmetry given by \(\widehat{asym}_{d}=\widehat{\boldsymbol p}^\top (\boldsymbol J-\boldsymbol I)\boldsymbol D\widehat{\boldsymbol p}\),
where \(\widehat{\boldsymbol p}=(\widehat{p}_0, \widehat{p}_1, \ldots, \widehat{p}_n)^\top\),
with \(\widehat{p}_k\) being the standard estimate of the marginal probability for state
\(s_k\), \(\boldsymbol I\) and \(\boldsymbol J\) are the identity and counteridentity
matrices of order \(n + 1\), respectively, and \(\boldsymbol D\) is a pairwise distance
matrix for the elements in the set \(\mathcal{S}\) considering a specific distance
between ordinal states, \(d(\cdot, \cdot)\). If normalize = TRUE, then the normalized estimate is computed, namely
\(\frac{\widehat{asym}_{d}}{max_{s_i, s_j \in \mathcal{S}}d(s_i, s_j)}\).