How to approximate a distribution using a random perturbation of the distribution - MathOverflow 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 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>