Yes, it is possible to simulate multivariate copulas beyond the Gaussian, Student-t, or Archimedean families in MATLAB, including the Farlie-Gumbel-Morgenstern (FGM) and Cuadras-Augé families. However, MATLAB's built-in functionality for copulas is limited to the more common families, so for less common copulas like FGM or Cuadras-Augé, you would typically need to implement the simulation yourself or look for third-party implementations.
Here's a simple MATLAB function to simulate a bivariate FGM copula:
function [X, Y] = simulateFGMCopula(n, theta)
% n is the number of samples to generate
% theta is the dependence parameter of the FGM copula
% Step 1: Generate independent uniform random numbers
U = rand(n, 1);
V = rand(n, 1);
% Step 2: Apply the FGM copula formula
% For the bivariate case, we use the CDF directly to calculate the joint distribution.
% This is specific to the FGM copula and would be different for other copula types.
% Note: The FGM copula is only valid for -1 <= theta <= 1.
C = U .* V + theta .* U .* V .* (1 - U) .* (1 - V);
% Step 3: Apply the inverse of the marginals (if non-uniform marginals are desired)
% For example, if X and Y are normally distributed with mean 0 and standard deviation 1:
X = norminv(U, 0, 1);
Y = norminv(V, 0, 1);
% If you want to keep U and V as uniform marginals, you can simply return them:
% X = U;
% Y = V;
end
For the Cuadras-Augé family and other more complex or less common copulas, you would need to derive the appropriate simulation procedure based on the copula's definition and properties. This might involve more sophisticated sampling methods, such as Markov Chain Monte Carlo (MCMC) or other numerical techniques.
If you're looking for a more advanced or specific implementation, you may need to search for academic papers, specialized toolboxes, or contributions from the MATLAB community that provide code for these less common copulas.
