Moment Conversion Functions

mathStatica allows one to express any moment (raw , central μ, or cumulant κ) in terms of any other moment (, μ, or κ). For instance, to express the second central moment (the variance) in terms of raw moments, we enter:

This is just the well-known result that . 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 expressed in terms of trivariate cumulants: