I know that if I want to transform some data points to a mean of zero and standard deviation to 1 I can use this formula:
$$Z= \frac{x-μ}{σ}$$
However if for example I want for example to normalize my data in such a way so that:
$$E[X^3]=a$$ I am not aware or was able to find or come up with a formula/transform that can do such a thing
Also, how do I generalize this to higher moments transform? $$E[X^n]=a_n$$ Any formulas, derivations and explanations are highly appreciated!