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Computing Relations between Moments and Cumulants

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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.

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References

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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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  1. Division of Biometry and Risk Assessment, National Center for Toxicological Research, Jefferson, AR, 72079, USA

    Qi Zheng

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  1. Qi Zheng
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Zheng, Q. Computing Relations between Moments and Cumulants. Computational Statistics 17, 507–515 (2002). https://doi.org/10.1007/s001800200123

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