High Quality Content by WIKIPEDIA articles! In statistics, a mixture density is a probability density function which is expressed as a convex combination (i.e. a weighted sum, with non-negative weights that sum to 1) of other probability density functions. The individual density functions that are combined to make the mixture density are called the mixture components, and the weights associated with each component are called the mixture weights. Any mixture density can be interpreted as "first, pick randomly among the components according to a distribution defined by the mixture weights (i.e. a categorical distribution), then pick from the chosen probability distribution to get a sample". Due to this interpretation as a two-step process, it is always possible to interpret a mixture density as the distribution resulting from a simple two-step hierarchical model, termed a mixture model. See also the article on mixture models, as well as the general article on graphical models.

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