Methodology and Computing in Applied Probability

, Volume 17, Issue 3, pp 541-564

First online:

Moments and Cumulants of a Mixture

  • Christopher S. WithersAffiliated withApplied Mathematics Group, Industrial Research Limited
  • , Saralees NadarajahAffiliated withSchool of Mathematics, University of Manchester Email author 
  • , Shou Hsing ShihAffiliated withDepartment of Mathematics and Statistics, American University of Sharjah

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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