How signal moments work?
I dont think there is a common framework for defining all those operators. Each of them were developed by different people, at several moments of the history. They are being integrated day by day onto a common discipline called DSP.  

As clarification, an operator (like a moment or any other) and the "redundancy" of a signal are very different and unrelated concepts. 

IF you want a deeper answer, list all the moments you are considering, and all the different math theories you are reviewing for each of them.