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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).
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Is every piecewise distribution a mixture distribution?
If I have a piecewise distribution with density $f$ on $[0,1)$ so that $f=f_1$ on $[0,0.5)$ and $f=f_2$ on $[0.5,1)$, with both $f_1$ and $f_2$ densities, is it necessarily a mixture distribution? My …