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Piecewise distribution
How can I write a piecewise distribution?
I want a distribution that consists of 3 distributions, each defined on it's range:
{ Gamma(a-, b-)(-x), when x < 0
y = { 0, when x = 0
{ Gamma(a+, b+)(x), when x > 0
It looks like a mixture of a Deterministic and a two-piece distribution, similar to TwoPieceNormal or TwoPieceStudentT, but with 2 Gamma functions.
Is it possible to define a piecewise distribution similar way to defining a Mixture? Or is is possible to build it by writing a transformation of some existing "TwoPiece" distribution?