非中心威沙特分布矩的图形表示及其应用
Graph presentations for moments of noncentral Wishart distributions and their applications
摘要：
本文给出了一般次数的实和复非中心威沙特分布的矩公式。所得到的公式，为真正的和复杂的情况下描述的无向图和有向图，分别。考虑退化情形，通过枚举图给出了二元χ 2分布和$2\times 2$ Wishart分布的矩的显式表达式.注意到拉盖尔多项式可以被认为是一个非中心χ 2分布的时刻，我们证明了一个组合的解释系数的拉盖尔多项式。
英文摘要：
We provide formulas for the moments of the real and complex noncentral Wishart distributions of general degrees. The obtained formulas for the real and complex cases are described in terms of the undirected and directed graphs, respectively. By considering degenerate cases, we give explicit formulas for the moments of bivariate chi-square distributions and $2\times 2$ Wishart distributions by enumerating the graphs. Noting that the Laguerre polynomials can be considered to be moments of a noncentral chi-square distributions formally, we demonstrate a combinatorial interpretation of the coefficients of the Laguerre polynomials.
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