https://randomservices.org/random/dist/Mixed.html
Mixed distribution - a distribution in which the distribution function is a linear combination of other distribution functions. Without limiting generality, we can assume that each of them is no longer a linear combination of any other distribution functions.
If you start from the theory that covers all possible forms of probability distribution function on the real line, then you will find that that such functions can be classified according to three different types of component:
(1) discrete components, where the distribution function is discontinuous;
(2) a probability density component, where the distribution function is continuous and differentiable;
(3) a singular component, where the distribution function is continuous but not differentiable.
A general distribution function can be specified as being the weighted sum of these three different types. Statistical models usually only consider only distributions that are either pure forms of of he first two types, or are mixtures of the first two types. However, certain types of probability-based models can and do lead to distributions with singular components.
In standard terminology, a "mixed distribution" may mean that you are considering distribution functions of the above general type, or may mean a much more restricted set of component types, depending on context. One particular common usage is that it means a distribution function having a pure probability density representation which is itself specified as a weighted sum of simple probability density distributions.
It will be clear that considering probability distributions in their most general form over several variables would be much more complicated.
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