In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its definition by as many non-central ones. Specifically, a novel approach to tackling the analysis of this model is introduced based on a simple conditional density together with a suitable transposition into the non-central framework of a characterizing property of independent Chi-Squared random variables. This approach thus enables to remedy the undeniable mathematical complexity of the joint density function of such distribution by paving the way towards achieving a new attractive stochastic representation as well as a surprisingly simple closed-form expression for its mixed raw moments.

翻译：本文件提供了对非中央Drichlet分布研究的新见解,后者是Drichlet分布的类比,它通过以许多非中央变量取代其定义中涉及的Chi-Squarid随机变量而获得的Drichlet分布,具体地说,在简单条件密度的基础上,采用了一种新颖的方法处理这一模型的分析,同时将一个适当的转换到非中央框架,将独立的Chi-Squaried随机变量特性定性,从而能够纠正这种分布的不可否认的数学复杂性,通过为实现新的有吸引力的随机代表以及令人惊讶的复杂原始时的封闭式表达方式铺平道路。