Moment Conversion Functions

mathStatica allows one to express any moment (raw [Graphics:Images/index_gr_1.gif], central μ, or cumulant κ) in terms of any other moment ([Graphics:Images/index_gr_2.gif], μ, or κ). For instance, to express the second central moment (the variance) [Graphics:Images/index_gr_3.gif] in terms of raw moments, we enter:


This is just the well-known result that [Graphics:Images/index_gr_6.gif]. As a further example, here is the sixth cumulant expressed in terms of raw moments:


The moment converter functions are completely general, and extend in the natural manner to a multivariate framework. Here is the trivariate central moment [Graphics:Images/index_gr_9.gif] expressed in terms of trivariate cumulants: