# Request for Multi-dimensional simulation reference book

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.

• 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? – Xi'an May 13 '17 at 11:40

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.