# why when I use mvrnd to generate random vectors from a multivariate normal I always get small numbers in absolute value ?

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MRC on 11 Dec 2013
Edited: Vaclav Rimal on 11 Dec 2013
Hi, why when I use mvrnd to generate random vectors from a multivariate normal I always get small numbers in absolute value (not larger than 4 or 5)? E.g.
mu=[0 0];
sigma=[1 0.4; 0.4 1];
r=10000; %number of simulated unobservables
epsilon=mvnrnd(mu,sigma,r);
Thanks

Vaclav Rimal on 11 Dec 2013
The width of the distribution is ruled by the diagonal elements of sigma. If you want larger absolute values, try scaling sigma, e.g.
sigma = [10 4; 4 10];
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Vaclav Rimal on 11 Dec 2013
Edited: Vaclav Rimal on 11 Dec 2013
But when the variances are v=1.0, the standard deviations of both vectors are supposed to be sqrt(v)=1.0, so there is only a little probability that a value exceeds the number 5 you mentioned. (99.7 % should have absolute values less than 3*sqrt(v), which you can test by sum(abs(epsilon)<3).) You simply cannot have v=1.0 and large numbers in the result.