Piecewise distribution

[Strategy24]

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?