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

Creators: Ouimet, Frédéric

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.

Additional Information

© 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Received: 10 November 2020; Accepted: 5 January 2021; Published: 6 January 2021. We thank the three referees for their comments. Author Contributions: All contributions were made by the sole author of the article, F.O. The author has read and agreed to the published version of the manuscript. This research was funded by a postdoctoral fellowship from the NSERC (PDF) and a postdoctoral fellowship supplement from the FRQNT (B3X). The author declares no conflict of interest.

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