(un)Evenness

dissimilarity (distribution, classes=None)

The index, popularised by Duncan & Duncan in 1955, measures the difference in concentration between the different categories.

The dissimilarity between the categories $\alpha$ and $\beta$ is defined as

$$D_{\alpha \beta} = \frac{1}{2} \sum_{t=1}^T \left| \frac{n_\alpha(t)}{N_\alpha} - \frac{n_\beta(t)}{N_\beta} \right|$$

By construction, we have $D \in \left[0, 1\right]$, with $D=1$ when the categories are never present in the same areal units (perfect segregation) and $D=0$ when their respective concentrations are identical in all units.

Parameters

• distribution dictionary

  Takes a dictionary of dictionaries with
  distribution[areal_unit][category] = number

• classes dictionary, optional

  Takes a dictionary of lists with classes[class] = [cat1, cat2, ...]
  If not specified, the algorithm will use the categories found in distribution

Output

• dissimilarity

  Returns a dictionary of dictionaries with
  dissimilarity[alpha][beta] = $D_{\alpha \beta}$