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how to work with custom probability distributions
Mathematica knows a lot of probability distributions and operations on them such as their cumulative distribution function, its converse, convolutions, etc. In my application, I need custom distributions given by finitely many atoms on a lattice and/or a piecewise Lebesgue density. Various other distributions are then defined in terms of these: If X, Y, Z are real-valued independent, I need the distribution of complex expressions such as X/Y*Boole[Z<0]+X*Y*const*Boole[Z>=0]. How do I define probability measures, except by implementing everything from scratch? How do I make the builtins operate on them? How do I get "composite" distributions, except by doing the math myself?