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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

1. Heidari, Hadi; Arabi, Mazdak; Ghanbari, Mahshid; Warziniack, Travis (June 2020). "A Probabilistic Approach for Characterization of Sub-Annual Socioeconomic Drought Intensity-Duration-Frequency (IDF) Relationships in a Changing Environment". Water. 12 (6): 1522. doi:10.3390/w12061522.

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

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