Hi Kulldep,

You can use this function.

##First generate a vector. Call it "x".

##And define this function (simcor). This function will return a vector (y) which ##correlated with choosen level.

simcor

Two valid answers came up, with different solutions:

Thank you Anna Mueller-Schoell, it works.

Thanks Hüseyin Yıldız , your code gives the desired result.

More generally, a multivariate normal variable X with k dimensions, and covariance matrix Σ = LLT, can be generated by starting with a vector Y of k independent normal variables with variance 1, and using the following theorem.

Theorem. If Σ = LLT, then the covariance matrix of X = LY is Σ.

For random variables with beta or gamma distribution, I propose an algorithm (see attached file), based on a work of Michael & Schucany (The mixture approach for simulating bivariate distributions with specified correlations, The American Statistician, 56 (1), 48-54). Instead of R programming, you can also test the following MATLAB® codes.

Regards, Bernd

% bivariate beta

a1=35;

a3=45;

b1=37;

b3=47;

rho=0.85;

n=round((a1+b1).*rho./(1-rho),0);

n_rep=1000000;

X1=zeros(n_rep,1);

X2=zeros(n_rep,1);

for i=1:n_rep

X1(i)=betarnd(a1,b1);

k=binornd(n,X1(i));

X2(i)=betarnd(a1+k,b1+n-k);

end

X2_index=(1:1:n_rep)';

X=[X2,X2_index];

[X_sort,index]=sortrows(X,1);

X3_a=betarnd(a3,b3,[n_rep,1]);

X3_sort=sort(X3_a);

X3=zeros(n_rep,1);

X3(index)=X3_sort;

---

% bivariate gamma

a1=50;

a3=55;

b1=0.019; l1=1./b1;

b3=0.022; l3=1./b3;

rho=0.95;

T=l1.*rho./(1-rho);

n_rep=1000000;

X1=zeros(n_rep,1);

X2=zeros(n_rep,1);

for i=1:n_rep

X1(i)=gamrnd(a1,b1);

k=poissrnd(T.*X1(i));

X2(i)=gamrnd(a1+k,1./(l1+T));

end

X2_index=(1:1:n_rep)';

X=[X2,X2_index];

[X_sort,index]=sortrows(X,1);

X3_a=gamrnd(a3,b3,[n_rep,1]);

X3_sort=sort(X3_a);

X3=zeros(n_rep,1);

X3(index)=X3_sort;

Thank you Bernd Meyer for providing more options.

Hello Fadhaa Ali

Kuldeep Kumar Tiwari, see the links below:

https://stats.stackexchange.com/questions/15011/generate-a-random-variable-with-a-defined-correlation-to-an-existing-variables

https://stats.stackexchange.com/questions/38856/how-to-generate-correlated-random-numbers-given-means-variances-and-degree-of

https://stats.stackexchange.com/questions/13382/how-to-define-a-distribution-such-that-draws-from-it-correlate-with-a-draw-from

Hope that helps.