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how to work with custom probability distributions

• To: mathgroup at smc.vnet.net
• Subject: [mg111556] how to work with custom probability distributions
• From: TJR <tilminator at googlemail.com>
• Date: Thu, 5 Aug 2010 06:59:30 -0400 (EDT)

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?