Graph presentations for moments of noncentral Wishart distributions and their applications |
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| Authors: | Satoshi Kuriki Yasuhide Numata |
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| Institution: | 1.The Institute of Statistical Mathematics, ROIS,Tokyo,Japan;2.Department of Mathematical Informatics,The University of Tokyo,Tokyo,Japan;3.Japan Science and Technology Agency (JST), CREST,Tokyo,Japan |
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| Abstract: | 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. |
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