New formulas for the moments about zero of the Non-central Chi-Squared and the Non-central Beta distributions are achieved by means of novel approaches. The mixture representation of the former model and a new expansion of the ascending factorial of a binomial are the main ingredients of the first approach, whereas the second one hinges on an interesting relationship of conditional independence and a simple conditional density of the latter model. Then, a simulation study is carried out in order to pursue a twofold purpose: providing numerical validations of the derived moment formulas on one side and discussing the advantages of the new formulas over the existing ones on the other.

翻译：以创新方法实现中子平方零分和中贝塔非中位分布时的新公式。前一种模式的混合表示和二进制要素上升因素的新的扩展是第一种方法的主要成份,而第二种则取决于有条件独立和后一种模式简单有条件密度的有趣关系。然后,进行模拟研究,以追求双重目的:一方面提供衍生瞬时公式的数值验证,另一方面讨论新公式相对于现有公式的优势。