Graph presentations for moments of noncentral Wishart distributions and their applications
Graph presentations for moments of noncentral Wishart distributions and their applications
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DOI：
10.1007/s10463-010-0279-4
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发表时间：
2009-12
影响因子：
1
通讯作者：
S. Kuriki;Yasuhide Numata
中科院分区：
文献类型：
--
作者：
S. Kuriki;Yasuhide Numata
我们提供了一般度数的实数和复数非中心 Wishart 分布的矩公式。所获得的真实情况和复杂情况的公式分别用无向图和有向图来描述。通过考虑退化情况，我们通过枚举图给出了二元卡方分布和 2 × 2 Wishart 分布矩的显式公式。注意到拉盖尔多项式可以被认为是形式上的非中心卡方分布的矩，我们演示了拉盖尔多项式系数的组合解释。
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 × 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.