The Canberra distance is a sum-weighted version of the Manhattan distance as follows:
$$\sum\limits_{i=1}^n \frac{|p_i-q_i|}{|p_i|+|q_i|}$$
where $p$ and $q$ are two ranked lists or vectors.
Is there a way to compute the maximum possible distance of an ordered vector? e.g. if we have $(1,2,3,4,5)$ compared only with permutations of itself, what can be the maximum distance? My guess is that $(5,4,3,2,1)$ will be one of the permutations that will produce the maximum. However, is there any analytical way to do this?
The reason I as is I would like to normalize the distance between 0 and 1.