Mixture (probability)

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 sum of separate distributions (representing separate populations) and the task is to infer from which population each observation arises.