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. doi:10.3390/stats4010002. 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.
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| 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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| Issue or Number: | 1 | |||||||||
| DOI: | 10.3390/stats4010002 | |||||||||
| 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: | 16 Nov 2021 19:03 |
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