xskillscore.Contingency.gerrity_score¶

Contingency.gerrity_score()¶

Returns Gerrity equitable score for a contingency table with K categories.

\[GS = \frac{1}{N}\sum_{i=1}^{K}\sum_{j=1}^{K}n(F_i, O_j)s_{ij}\]

\[s_{ii} = \frac{1}{K-1}(\sum_{r=1}^{i-1}a_r^{-1} + \sum_{r=i}^{K-1}a_r)\]

\[s_{ij} = \frac{1}{K-1}(\sum_{r=1}^{i-1}a_r^{-1} - (j - i) + \sum_{r=j}^{K-1}a_r);\, 1 \leq i < j \leq K\]

\[s_{ji} = s_{ij}\]

\[a_i = \frac{(1 - \sum_{r=1}^{i}p_r)}{\sum_{r=1}^{i}p_r}\]

\[p_i = \frac{N(O_i)}{N}\]

References