Editing Mixture distribution (section)

== Applications ==
{{Further|Mixture model}}

Mixture densities are complicated densities expressible in terms of simpler densities (the mixture components), and are used both because they provide a good model for certain data sets (where different subsets of the data exhibit different characteristics and can best be modeled separately), and because they can be more mathematically tractable, because the individual mixture components can be more easily studied than the overall mixture density.

Mixture densities can be used to model a [[statistical population]] with [[subpopulation]]s, where the mixture components are the densities on the subpopulations, and the weights are the proportions of each subpopulation in the overall population.

Mixture densities can also be used to model [[experimental error]] or contamination – one assumes that most of the samples measure the desired phenomenon, with some samples from a different, erroneous distribution.

Parametric statistics that assume no error often fail on such mixture densities – for example, statistics that assume normality often fail disastrously in the presence of even a few [[outliers]] – and instead one uses [[robust statistics]].

In [[meta-analysis]] of separate studies, [[study heterogeneity]] causes distribution of results to be a mixture distribution, and leads to [[overdispersion]] of results relative to predicted error. For example, in a [[statistical survey]], the [[margin of error]] (determined by sample size) predicts the [[sampling error]] and hence dispersion of results on repeated surveys. The presence of study heterogeneity (studies have different [[sampling bias]]) increases the dispersion relative to the margin of error.