Introduction
Mixture distributions are convex combinations of “component” distributions. In statistics, these are standard tools for modeling heterogeneity in the sense that different elements of a sample may belong to different components. However, they may also be used simply as flexible instruments for achieving a good fit to data when standard distributions fail. As good software for fitting mixtures is available, these play an increasingly important role in nearly every field of statistics.
It is convenient to explain finite mixtures (i.e., finite convex combinations) as theoretical models for cluster analysis (see Cluster Analysis: An Introduction), but of course the range of applicability is not at all restricted to the clustering context. Suppose that a feature vector X is observed in a heterogeneous population, which consists of k homogeneous subpopulations, the “components.” It is assumed that for \(i = 1,\ldots ,k\), Xis distributed in the i-th component according to a...
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References and Further Reading
Böhning D (2000) Finite mixture models. Chapman and Hall, Boca Raton
Frühwirth-Schnatter S (2006) Finite mixture and Markov switching models. Springer, New York
Hennig C (2000) Identifiability of models for clusterwise linear regression. J Classif 17:273–296
Hennig C (2004) Breakdown points for ML estimators of location-scale mixtures. Ann Stat 32:1313–1340
Lindsay BG (1995) Mixture models: theory, geometry and applications. NSC-CBMS Regional Conference Series in Probability and Statistics, 5
McLachlan GJ, Peel D (2000) Finite mixture models. Wiley, New York
Schlattmann P (2009) Medical applications of finite mixture models. Springer, Berlin
Titterington DM, Smith AFM, Makov UE (1985) Statistical analysis of finite mixture distributions, Wiley, New York
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Seidel, W. (2011). Mixture Models. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_368
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DOI: https://doi.org/10.1007/978-3-642-04898-2_368
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