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

Department of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA
Received: 10 November 2020 / Revised: 31 December 2020 / Accepted: 5 January 2021 / Published: 6 January 2021
(This article belongs to the Section Multivariate Analysis)
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. View Full-Text
Keywords: multinomial distribution; higher moments; central moments; non-central moments multinomial distribution; higher moments; central moments; non-central moments
MDPI and ACS Style

Ouimet, F. General Formulas for the Central and Non-Central Moments of the Multinomial Distribution. Stats 2021, 4, 18-27. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010002

AMA Style

Ouimet F. General Formulas for the Central and Non-Central Moments of the Multinomial Distribution. Stats. 2021; 4(1):18-27. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010002

Chicago/Turabian Style

Ouimet, Frédéric. 2021. "General Formulas for the Central and Non-Central Moments of the Multinomial Distribution" Stats 4, no. 1: 18-27. https://0-doi-org.brum.beds.ac.uk/10.3390/stats4010002

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