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Can anybody give proof of the above relationship algebraically?I have not seen the derivation of it.
I was in a hurry and when one is not familiar with the derivation ,often one messes the formula.I don't think that this is a generally valid relationship. I would guess that it holds for a PDF expressed in terms of a lowest order Edgeworth series.
Oh sorry we posted at the same time just seconds delay.Can you give the proof using algebraic manipulation other than using variance or standard deviation?I found also this interesting discussion:
http://stats.stackexchange.com/questions/3787/empirical-relationship-between-mean-median-and-mode
I have seen that link in Mathematics stack exchange before and I did't get it that's why I have posted it here.When you first posted that it is not a valid relationship I thought that modification in statistic may have came for this formula.I hardly know more about this relation than you. In the link I found there are all the references to original articles you need.