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

Frédéric Ouimet
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Frédéric Ouimet: Department of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA

Stats, 2021, vol. 4, issue 1, 1-10

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.

Keywords: multinomial distribution; higher moments; central moments; non-central moments (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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