Normal Mixtures

  • Bernard Flury
Part of the Springer Texts in Statistics book series (STS)


This chapter gives a brief introduction to theory and applications of finite mixtures, focusing on the most studied and reasonably well-understood case of normal components. An introductory example has already been given in Chapter 1 (Example 1.3) and has been discussed to some extent in Section 2.8, where the relevant terminology has been established. Before turning to the mathematical setup, let us look at yet another example to motivate the theory.


Discriminant Analysis Wing Length Finite Mixture Mixture Density Normal Mixture 
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Suggested Further Reading

  1. Everitt, B.S., and Hand, D.J. 1981. Finite Mixture Distributions. London: Chapman and Hall.MATHCrossRefGoogle Scholar
  2. McLachlan, G.J., and Basford, K.E. 1988. Mixture Models: Inference and Applications to Clustering. New York: Dekker.MATHGoogle Scholar
  3. Titterington, D.M., Smith, A.F.M., and Makov, U.E. 1985. Statistical Analysis of Finite Mixture Distributions. New York: Wiley.MATHGoogle Scholar
  4. Day, N.E. 1969. Estimating the components of a mixture of normal distributions. Biometrika 56, 464–474.Google Scholar
  5. Dempster, A.P., Laird, N.M., and Rubin, D.B. 1977. Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society Series B, 39, 1–38.MathSciNetMATHGoogle Scholar
  6. McLachlan, G.J., and Krishnan, T. 1997. The EM Algorithm and Extensions. New York: Wiley.MATHGoogle Scholar
  7. Airoldi, J.-P., Flury, B., and Salvioni, M. 1996. Discrimination between two species of Microtus using both classified and unclassified observations. Journal of Theoretical Biology 177, 247–262.CrossRefGoogle Scholar
  8. O’Neill, T.J. 1978. Normal discrimination with unclassified observations. Journal of the American Statistical Association 73, 821–826.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • Bernard Flury
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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