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A non-recursive formula for various moments of the multivariate normal distribution with sectional truncation

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  • Ogasawara, Haruhiko

Abstract

A unified formula for various moments of the multivariate normal distribution with sectional truncation is derived using a non-recursive method, where sectional truncation is given by several sections (regions) for selection including single and double truncation as special cases. The moments include raw, central, arbitrarily deviated, non-absolute, absolute and partially absolute moments with non-integer orders for variables taking absolute values. The formula is alternatively shown using weighted Kummer’s confluent hypergeometric function and, in the bivariate case, the weighted Gauss hypergeometric function, where the weighted functions have advantages of fast convergence. Numerical illustrations with simulations show that the methods employed are relatively free from accumulating cancellation errors.

Suggested Citation

  • Ogasawara, Haruhiko, 2021. "A non-recursive formula for various moments of the multivariate normal distribution with sectional truncation," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:jmvana:v:183:y:2021:i:c:s0047259x21000075
    DOI: 10.1016/j.jmva.2021.104729
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    References listed on IDEAS

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    Cited by:

    1. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.
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    3. Christopher J. Adcock, 2022. "Properties and Limiting Forms of the Multivariate Extended Skew-Normal and Skew-Student Distributions," Stats, MDPI, vol. 5(1), pages 1-42, March.
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    6. Galarza, Christian E. & Matos, Larissa A. & Castro, Luis M. & Lachos, Victor H., 2022. "Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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