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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.

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.

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.mathematically. Alternatively, look into whether R can do this.