Before revision:  Refined } bounds for the absolute moments \mathbb{E[ |X^k-\operatorname{rd}(X)^{k}| ] } [ |X^k-\operatorname{rd}(X)^{k}|] } are also given.
After revision:  Refined } bounds for the absolute moments \mathbb{E[ |X^k-\operatorname{rd}(X)^{k}| ] } \mathbb{E[ |X^k-\operatorname{rd}(X)^{k}|] } are also given.