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General Formulas for the Central and Non-Central Moments of the Multinomial Distribution

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  • Frédéric Ouimet

    (Department of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA)

Abstract

We present the first general formulas for the central and non-central moments of the multinomial distribution, using a combinatorial argument and the factorial moments previously obtained in Mosimann (1962). We use the formulas to give explicit expressions for all the non-central moments up to order 8 and all the central moments up to order 4. These results expand significantly on those in Newcomer (2008) and Newcomer et al. (2008), where the non-central moments were calculated up to order 4.

Suggested Citation

  • Frédéric Ouimet, 2021. "General Formulas for the Central and Non-Central Moments of the Multinomial Distribution," Stats, MDPI, vol. 4(1), pages 1-10, January.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:1:p:2-27:d:475754
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    References listed on IDEAS

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