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
Article

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
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Abstract

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.

Keywords

Bell polynomialsCPU timeCumulantsMixturesMoments

AMS 2000 Subject Classification

62F03

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