How do pieces of a file in a torrent be shared non-uniformly?

Question

I sometimes see that pieces of a torrent file is not equally distributed. Since the pieces of an individual file are randomly chosen, I would expect a uniform distribution under the standard torrent protocol. But that isn't the case all the time. Starting, ending or a middle part of a file rarely happens to be shared more than the other parts. This is practically impossible, but it indeed occurs.

I would like to hear an explanation for this. What does cause this phenomenon?