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Graph presentations for moments of noncentral Wishart distributions and their applications

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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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Authors and Affiliations

  1. The Institute of Statistical Mathematics, ROIS, 10-3 Midori-cho, Tachikawa, Tokyo, 190-8562, Japan

    Satoshi Kuriki

  2. Department of Mathematical Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Yasuhide Numata

  3. Japan Science and Technology Agency (JST), CREST, Sanbancho, Chiyoda-ku, Tokyo, 102-0075, Japan

    Satoshi Kuriki & Yasuhide Numata

Authors
  1. Satoshi Kuriki
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  2. Yasuhide Numata
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Correspondence to Satoshi Kuriki.

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Kuriki, S., Numata, Y. Graph presentations for moments of noncentral Wishart distributions and their applications. Ann Inst Stat Math 62, 645–672 (2010). https://doi.org/10.1007/s10463-010-0279-4

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  • DOI: https://doi.org/10.1007/s10463-010-0279-4

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