Mixture (probability)

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

• A mixture defining a new probability distribution from some existing ones, as in a mixture distribution or a compound distribution. Here a major problem often is to derive the properties of the resulting 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 of several components, and the problem is that of a mixture model, in which the task is to infer from which of a discrete set of sub-populations each observation originated.

See also

• Mixture distribution
• Compound distribution
• Mixture model
• classification
• Cluster analysis
• Giry monad

References

• Yao, Weixin; Xiang, Sijia (2024), Mixture Models: Parametric, Semiparametric, and New Directions, Boca Raton, FL: Chapman & Hall/CRC Press, ISBN 978-0367481827.