A mixture distribution is one that is written as a convex combination of other distributions. Use the "compound-distributions" tag for "concatenations" of distributions (where a parameter of a distribution is itself a random variable).
Mixture models arise in attempts to characterize complicated probability distributions, especially those with two or more modes, in terms of distributions with mathematically simple descriptions.
Disambiguation
Do not confuse a "mixture model" with a "mixed model"! The former concerns distributions, typically multi-modal, that will be analyzed as positive linear combinations of other distributions. The latter occurs in a regression setting where some of the independent variables are viewed as fixed and others are viewed as realizations of random variables.
Note that although the density of a mixture is, by definition, a linear combination of densities, it is not in general the same as the density of a linear combination of random variables. For example, the average of two normal random variables is normal (and therefore has a single mode), but a 50:50 mixture of two different normal densities often has two modes and is never normal.
Compound distributions are also known as "mixtures". Please use the compound-distributions tag in such cases. See the meta thread on The “mixture” vs. the “compound-distributions” tags for details.
