How can I find the probability density function of the following function of two random variables x and y
z = 1 + ax + ax/(1 + by) + acy/(1 + by) + a^2 x^2/(1 + by)
where x and y are chi-square random variables and a, b and c are constants?
How can I find the probability density function of the following function of two random variables x and y
z = 1 + ax + ax/(1 + by) + acy/(1 + by) + a^2 x^2/(1 + by)
where x and y are chi-square random variables and a, b and c are constants?
This looks like a mess. It's certainly not a linear combination, so I would try the MGF technique, but most likely that will be nasty too.
If you want to use Jacobians, I would combine a couple of terms.
The third and fifth terms are tough since they have both x's and y's in them.