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A trivariate chi-squared distribution derived from the complex Wishart distribution

Author

Listed:
  • Hagedorn, M.
  • Smith, P.J.
  • Bones, P.J.
  • Millane, R.P.
  • Pairman, D.

Abstract

The joint density for a particular trivariate chi-squared distribution given by the diagonal elements of a complex Wishart matrix is derived. This distribution has applications in the processing of multilook synthetic aperture radar data. The expression for the density is in the form of an infinite series that converges rapidly and is simple and fast to compute. The expression is shown to reduce to known forms for a number of special cases and is validated by simulation. The characteristic function is also derived and used to relate joint moments of the trivariate distribution to the parameters of the density function.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:3:p:655-674
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    References listed on IDEAS

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    1. Royen, T., 1991. "Expansions for the multivariate chi-square distribution," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 213-232, August.
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    Cited by:

    1. Withers, Christopher S. & Nadarajah, Saralees, 2012. "Moments and cumulants for the complex Wishart," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 242-247.
    2. Dharmawansa, Prathapasinghe & McKay, Matthew R., 2009. "Diagonal distribution of a complex non-central Wishart matrix: A new trivariate non-central chi-squared density," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 561-580, April.
    3. Abraão Nascimento & Jodavid Ferreira & Alisson Silva, 2023. "Divergence-based tests for the bivariate gamma distribution applied to polarimetric synthetic aperture radar," Statistical Papers, Springer, vol. 64(5), pages 1439-1463, October.

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