I have a dataset consisting of hundreds of repeat observations on thousands of agents. Each observation is a ratio between two distance measures, A and B, where A is always larger than B. Thus, my observations have a lower bound of 1. I'd like to identify agents who's distributions are anomalous. In particular, I'd like to find agents who's distributions have anomalously high means compared to the other agents. I have no knowledge of how many types of agents there are, nor what proportion of my sample each (unknown) agent type comprises. Can someone suggest techniques/papers related to this problem?
There i no general shape or ratio distribution, this really depends on what the two factors were distributed like.
In many cases, ratio values become easier to handle when taking the logarithm. Since 1 is a lower bound, the log values will have 0 as lower bound. Thus, the result cannot be normal distributed, but it may be "normal enough" for regular techniques to work.
Try going to logspace, and visualize your data.