In
probability theory and
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, 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
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...
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
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model repres ...
such as is often used for
statistical classification. The model may represent the population from which observations arise as a
mixture
In chemistry, a mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the ...
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 Classification is a process related to categorization, the process in which ideas and objects are recognized, differentiated and understood.
Classification is the grouping of related facts into classes.
It may also refer to:
Business, organizat ...
*
Cluster analysis
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of ...
References
Probability theory
Compound probability distributions
Statistical classification
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