1 | initial version |

This question should go into math stack exchange. The formula/transformation you are looking for is the one with the Jacobian, not the one with the Dirac Delta function.

2 | No.2 Revision |

This question should go into math stack exchange. The formula/transformation you are looking for is the one with the Jacobian, not the one with the Dirac Delta function.

For two variables, you can define another function `Z = g(X,Y)`

which along with `W = h(X,Y)`

is bijective and differentiable (as explained in Wikipedia). Then the Jacobian will work and you can later integrate over `Z`

to get `W`

.

In terms of computing it, I am not aware of anything which can easily compute these distributions/densities. You are probably better off deriving it mathematically.

3 | No.3 Revision |

For two variables, you can define another function `Z = g(X,Y)`

which along with `W = h(X,Y)`

is bijective and differentiable (as explained in Wikipedia). Then the Jacobian will work and you can later integrate over `Z`

to get `W`

.

In terms of computing it, I am not aware of anything which can easily compute these distributions/densities. You are probably better off deriving it ~~mathematically.~~mathematically. Alternatively, look into whether R can do this.

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