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Moments and cumulants for the complex Wishart

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  • Withers, Christopher S.
  • Nadarajah, Saralees

Abstract

We summarize the main results known for the complex normal and complex Wishart, then give the cumulants of the central and noncentral complex Wishart. Their moments are expressed explicitly in terms of multivariate Bell polynomials, believed to be used here for the first time. Multivariate Bell polynomials are easily written down from their univariate forms, which are widely accessible in most computer algebra packages. This is shown to be the natural way of obtaining the moments for any sum of independent and identically distributed (i.i.d.) random variables. An extension is given to the weighted complex Wishart.

Suggested Citation

  • Withers, Christopher S. & Nadarajah, Saralees, 2012. "Moments and cumulants for the complex Wishart," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 242-247.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:242-247
    DOI: 10.1016/j.jmva.2012.05.002
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    References listed on IDEAS

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    1. Shaman, Paul, 1980. "The inverted complex Wishart distribution and its application to spectral estimation," Journal of Multivariate Analysis, Elsevier, vol. 10(1), pages 51-59, March.
    2. Fumiko Hirakawa, 1975. "Some distributions of the latent roots of a complex wishart matrix variate," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 357-363, December.
    3. Smith, Peter J. & Garth, Lee M., 2007. "Distribution and characteristic functions for correlated complex Wishart matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 661-677, April.
    4. Hagedorn, M. & Smith, P.J. & Bones, P.J. & Millane, R.P. & Pairman, D., 2006. "A trivariate chi-squared distribution derived from the complex Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 655-674, March.
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    Cited by:

    1. Di Nardo, Elvira, 2014. "On a symbolic representation of non-central Wishart random matrices with applications," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 121-135.

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