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Explicit formulae for product moments of multivariate Gaussian random variables

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  • Song, Iickho
  • Lee, Seungwon

Abstract

Explicit formulae for the product moments of multivariate Gaussian random variables are derived. The formulae we have discovered are more compact than other well-known ones and allow us to instantly evaluate any term of the product moments.

Suggested Citation

  • Song, Iickho & Lee, Seungwon, 2015. "Explicit formulae for product moments of multivariate Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 27-34.
    • Handle: RePEc:eee:stapro:v:100:y:2015:i:c:p:27-34
    DOI: 10.1016/j.spl.2015.01.030
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    References listed on IDEAS

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    1. Schott, James R., 2003. "Kronecker product permutation matrices and their application to moment matrices of the normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 177-190, October.
    2. Kan, Raymond, 2008. "From moments of sum to moments of product," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 542-554, March.
    3. Blacher, René, 2003. "Multivariate quadratic forms of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 2-23, October.
    4. Willink, R., 2005. "Normal moments and Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 271-275, July.
    5. Berkane, Maia & Bentler, P. M., 1986. "Moments of elliptically distributed random variates," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 333-335, October.
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    Cited by:

    1. Sikora, Grzegorz, 2018. "Statistical test for fractional Brownian motion based on detrending moving average algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 54-62.
    2. Baishuai Zuo & Chuancun Yin & Narayanaswamy Balakrishnan, 2020. "Explicit expressions for joint moments of $n$-dimensional elliptical distributions," Papers 2007.09349, arXiv.org, revised Aug 2020.

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