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# How to approximate distribution distribution using a random perturbation of the distribution

Suppose $f(0)=0$ and you want to simulate $f(Z)$ for some random variate $Z$ that you can generate. However, you can only obtain values of $f(Y+Z)$ and $f(Y)$ for some other variate $Y$. This feels like a standard problem that may even have a name. If so what is it called? If not, what can one do to approximate $f(Z)$?

I should also note that I'm particularly interested in tail values of $f(Z)$ but any approximation ideas would be useful.

I should also, also note that you may not use $Y$ or $Z$ or any metric on them. You can only use the values $f(Y+Z)$ and $f(Y)$ that you simulate. I'm thinking this almost kills any approximation possibilities but maybe there is some way of using the $f(0)=0$ property.