 For "n" = 1, the "n"th cumulant is just the expected value; for "n" = either 2 or 3, the "n"th cumulant is just the "n"th central moment; for "n" ≥ 4, the "n"th cumulant is an "n"th-degree monic polynomial in the first "n" moments (about zero), and is also a (simpler) "n"th-degree polynomial in the first "n" central moments.Sometimes it is convenient to convert moments about the origin to moments about the mean.The general equation for converting the "n"th-order moment about the origin to the moment about the mean is

where "μ" is the mean of the distribution, and the moment about the origin is given by

For the cases "n" = 2, 3, 4 — which are of most interest because of the relations to variance, skewness, and kurtosis, respectively — this formula becomes (noting that formula_7 and formula_8)