I have two datasets, 'A' and 'B', comprising N measurements of one quantity, that I would like to compare to the results of a simulation, let's call this last dataset 'S'. This comparison got me thinking and I have the following questions (which are quite general I guess).
Is a dataset completely determined by its standardized moments? That is to say, given a dataset I can always calculate its zeroth order moment, the first, and so forth. If I were able to calculate them all, I'll have a function of the discrete variable 'q', the order of the standardized moment. Is this function unique? That is to say, is the following statement a mathematical truth: "if two datasets have the same standardized moments, the datasets are the same" ?
Of course, I'm looking for an educated answer on this but also for some references where I could read more about this subject.
Thanks in advance for all your help.