most recent 30 from http://mathoverflow.net 2013-05-21T21:22:17Z http://mathoverflow.net/feeds/question/107724 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107724/how-to-approximate-a-distribution-using-a-random-perturbation-of-the-distribution mathtick 2012-09-20T23:10:07Z 2012-12-12T15:55:00Z

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