Mixture (probability)

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For other uses, see mixture (disambiguation).

In probability theory and statistics, a mixture is a combination of two or more probability distributions. The concept arises in two contexts:

  • A mixture defining a new probability distribution from some existing ones, as in a mixture density. Here the main problem is to derive the theoretical properties of the new distribution.
  • A mixture used as a statistical model such as is often used for statistical classification.The model may represent the population from which observations arise as a mixture density, but the problem is that of a mixture model, in which a data classification hypothesis represents an overall distribution as a mixture of separate distributions (representing separate populations) and the task is to infer from which population each observation arises.