how to simulation data from a MULTIVARIATE log-normal distribution

You can use the rndMVn and exp functions to create multivariate lognormally distributed random deviates. For example:

//Covariance matrix
cov = { 1 0.6,
       0.6  1 };

//Mean for each column
mean = { 1, 1 };

//Create multivariate random normal numbers,/span>
x = rndMVn(1e6, mean, cov);

//normal -> lognormal
x_lognorm = exp(x);

You can calculate the mean and variance like this:

//Mean for normal numbers above
mean = 1;

//Variance for normal numbers above
variance = 1;

mean_lognorm = exp(mean + variance./2);

var_lognorm = (exp(variance) - 1) .* exp(2 .* mean + variance);

Based on the formulas above, the mean and variance for our example in the first code snippet should be approximately 4.48 and 34.51 (with a standard deviation of about 5.87).