1
$\begingroup$

Do you have any reference book about multi-dimensional simulation? The random variables are not identically distributed and are correlated.

I understand the procedure to generate correlated normal distributions but have no idea for this general cases.

Background: got a bachelor degree in mathematics.

$\endgroup$
  • $\begingroup$ The question is unclear: do you want to simulate a specific multivariate distribution, in which case how is it defined? Or do you ask for existing methods for standard distributions? $\endgroup$ – Xi'an May 13 '17 at 11:40
1
$\begingroup$

All books on simulation, like

contain entries on how to simulate joint distributions. Depending on how the joint distribution is defined, there are several general principles to produce such simulations:

  1. if the successive conditionals, $f_1(x_1)$, $f_2(x_2|x_1)$, $f_3(x_3|x_1,x_2)$, &tc., can be simulated, producing a joint simulation means simulating the first, then the second, &tc. univariate distributions;
  2. if the joint density $f(x_1,\ldots,x_n)$ is available in closed form, then different MCMC methods can be applied to this target as, e.g., the Gibbs sampler;
    1. if the joint distribution can be expressed as a copula, then simulation of a joint uniform over $[0,1]^n$ is sufficient, followed by a deterministic transform by the inverse cdf's for each component.
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.