Computing Relations between Moments and Cumulants
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It is sometimes desirable to have easily accessible formulae expressing moments in terms of cumulants and vice versa. This paper offers a Mathematica implementation of two methods for generating such formulae, a method based on Kendall’s operator and an elementary method of equating coefficients of generating functions.
Keywordssymbolic computing rewrite rule Kendall’s operator cumulant moment
This work originated from my participation in the 1995–1996 Mathematica Visiting Scholar Program sponsored by Wolfram Research Inc. I am indebted to Dr. K. Hutcheson for kindly providing me with a copy of Kratky et al. (1972). Several improvements in the presentation of the material in this article have resulted from suggestions by co-editor h. j. Newton, an associate editor, and a referee.
- Kratky, J., Reinfelds, J., Hutcheson, K. & Shenton, L. R. (1972), Tables of crude moments expressed in terms of cumulants, Technical report, University of Georgia, Athens, Georgia.Google Scholar
- Zheng, Q. (1998), Computing relations between statistical moments and cumulants, ‘Proceedings of the Computational Statistics Section’, American Statistical Association, pp. 165–170.Google Scholar