Mixture (probability)

{{one source |date=March 2024}}

In probability theory and statistics, a mixture is a probabilistic combination of two or more probability distributions.{{Cite journal|last1=Heidari|first1=Hadi|last2=Arabi|first2=Mazdak|last3=Ghanbari|first3=Mahshid|last4=Warziniack|first4=Travis|date=June 2020|title=A Probabilistic Approach for Characterization of Sub-Annual Socioeconomic Drought Intensity-Duration-Frequency (IDF) Relationships in a Changing Environment|journal=Water|language=en|volume=12|issue=6|pages=1522|doi=10.3390/w12061522|doi-access=free}} 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.