Advantage of central moment over moment?

Question

Is there any advantage of using "central moments" over "moments" when approximating a distribution to a known distribution using moment matching? I have noticed that in lot of papers.

Answer 1

Following the suggestion by gung:

Central moments $\mu_n$ are related to moments $m_n$ through linear transformations:

$$\mu_n = E[(X-\mu)^n] = \sum_{i=0}^n \binom{n}{i}(-\mu)^{n-i}E[X^i] = \sum_{i=0}^n \binom{n}{i}(-\mu)^{n-i}m_i.$$

An adaptation, emendation, and incorporation of a proposal by @Flav for an improved statement:

One theoretical advantage to central moments is that they are invariant to translations along the $x$ axis: the central moments of $Y = X + a$ are the same as the central moments of $X$. From a computational perspective, in some cases, (non-central) moments are slightly easier to calculate than central moments, while in other cases, the central moments are slightly easier to calculate.