title: Generating random values from non-normal and correlated distributions
body: <p>I have a random variable X that is a mixture of a binomial and two normals (see what the <a href="https://stackoverflow.com/questions/4454513/combining-two-normal-random-variables/4454941#4454941">probability density function would look like</a> (first chart))<br>
  and I have another random variable Y of similar shape but with different values for each normally distributed side.</p>
  
  <p>X and Y are also correlated, here's an example of data that could be plausible :</p>
  
  <pre><code>    X     Y
  1.  0    -20
  2. -5     2
  3. -30    6
  4.  7    -2
  5.  7     2
  </code></pre>
  
  <p>As you can see, that was simply to represent that my random variables are either a small positive (often) or a large negative (rare) and have a certain covariance.</p>
  
  <p>My problem is : I would like to be able to sample correlated and random values from these two distributions.</p>
  
  <p>I could use Cholesky decomposition for generating correlated <em>normally distributed</em> random variables, but the random variables we are talking here are not normal but rather a mixture of a binomial and two normals.</p>
  
  <p>Many thanks!</p>