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

Ouimet, Frédéric (2021) General Formulas for the Central and Non-Central Moments of the Multinomial Distribution. Stats, 4 (1). pp. 18-27. ISSN 2571-905X. https://resolver.caltech.edu/CaltechAUTHORS:20210113-112153856

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.3390/stats4010002DOIArticle
https://arxiv.org/abs/2012.13777arXivDiscussion Paper
ORCID:
AuthorORCID
Ouimet, Frédéric0000-0001-7933-5265
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.
Funders:
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Fonds de recherche du Québec – Nature et technologies (FRQNT)B3X
Issue or Number:1
Record Number:CaltechAUTHORS:20210113-112153856
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210113-112153856
Official Citation:Ouimet, F. General Formulas for the Central and Non-Central Moments of the Multinomial Distribution. Stats 2021, 4, 18-27
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107454
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Jan 2021 20:09
Last Modified:13 Jan 2021 20:09

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