Methodology and Computing in Applied Probability

, Volume 17, Issue 3, pp 541–564

Moments and Cumulants of a Mixture

  • Christopher S. Withers
  • Saralees Nadarajah
  • Shou Hsing Shih

DOI: 10.1007/s11009-013-9379-y

Cite this article as:
Withers, C.S., Nadarajah, S. & Shih, S.H. Methodol Comput Appl Probab (2015) 17: 541. doi:10.1007/s11009-013-9379-y


For the first time, general formulas for moments and cumulants are derived for mixtures of two or more distributions. The formulas involve the Bell polynomials. Computational efficiency of the formulas is illustrated by applications for two-component and three-component normal mixture models.


Bell polynomials CPU time Cumulants Mixtures Moments 

AMS 2000 Subject Classification


Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Christopher S. Withers
    • 1
  • Saralees Nadarajah
    • 2
  • Shou Hsing Shih
    • 3
  1. 1.Applied Mathematics GroupIndustrial Research LimitedLower HuttNew Zealand
  2. 2.School of MathematicsUniversity of ManchesterManchesterUK
  3. 3.Department of Mathematics and StatisticsAmerican University of SharjahSharjahUAE

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