Computational Statistics

, Volume 17, Issue 4, pp 507–515

# Computing Relations between Moments and Cumulants

• Qi Zheng
Article

## Summary

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.

## Keywords

symbolic computing rewrite rule Kendall’s operator cumulant moment

## Notes

### Acknowledgments

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.

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