Say I have a vector of length 1000. At each position (1 ... 1000) there is a count. I have two vectors with different range of counts such that in vector A the maximum number of counts at a position is 30, whereas in vector B the maximum is say 200 (i.e., there are more counts in B than A).
So essentially I have two discrete distributions and when I plot the two distributions they have peaks and troughs (some regions along the vector have higher counts than others). I am not interested in the differences in raw counts between A and B but instead wish to compare the shape of the curves in order to test whether the same regions (based on the index) in A and B have the higher counts relative to other regions.
My problem is that in order to compare the shapes I need to normalize the counts in each vector. I do not have have too much stats background and so any advice regarding an appropriate normalization procedure would be appreciated. The best, but probably not the best solution I can think of is to transform the vectors to have the same mean.