hi

I am working on project which requires Gamma RV generation. I need to
use C. H. Sim method of RV Generation.
Reference:

C. H. Sim "Generation of Poisson and Gamma Random Vectors with given
marginal and covariance matrix:
Journal of statistical Computation and simulation
Volume 47. no 1-2 Page 1-10 1993

i am wonding if has anyone tried this method and can provide me with a
code. I tried but seems to be wrong. I would appreciate if someone can
help with a code.

thanks
dhiraj

Hi chishmishdeez,

I have no access to the paper you mentioned, but I read a paper
entitled "Simulation of Nakagami Fading Channels With Arbitrary
Cross-Correlation and Fading Parameters" and used the equations
provided there (driven from Sim's method)for generating Gamma
vairates, and it worked.

By the way, may I know where you are from, your nick name seems to be
written in Pingilish!!

hi
yes i am talking about the same paper.
did that method work for first example they have given ?

thanks
Dhiraj

i Checked my code from few pplz they didnt find any bug
i dont know where i am wrong

How did u approach

What example you mean? There is just one example in which the Sim's
method used (that with deferent m-parameters) If you mean the first
verification example with m=2.18, the correlation coefficient matrix
in this case dose not satisfy the constraints for the Sim's method
given in (21) , (22) just before verification section, so it can't be
used for that.
If it is not your problem, may I know what is wrong with your results?

The Problem is although my code is correct, it is not able to generate
Gamma Vectors of proper statistical properties.i asked my friends to
check the implementation of Sim method but there is no problem.I dont
know where the problem lies.

Make sure that you are using the cross-covariance matrix in computing
the value a(i,j) of the matrix A, not the correlation coefficients
matrix. Notice that to compute a(i,j) from the recursive equation of
(19c), just previously computed element of i=2:N and j=2:i (N=number
of variates) are needed (the first column of A is computed by 19(b)).
Don't try to compute the others.
Hope this works; otherwise I can give you my code.

Hi
let me thank you for ur support.
let me check my code as per your instructions. and try one more time
whats happening. else i will contact you again
Thanks a lot
Dhiraj

hi
i would appreciate if u can send me ur code. 
thanks
DHiraj

Here is the code:

function Na = nakarnd(M, P, R, n);
% M:    m-parameter vector
% P:    power vector
% R:    correlation coefficient matrix
% n:    number of random variable samples

N = length(P);      % Number of variates
var = P.^2 ./ M;    % Variance of variates
covar = sqrt(diag(var)) * R * sqrt(diag(var));  % covariance matrix of variates.
l = M ./ P;     % lambda(i) = m(i)/P(i)
alpha = (1 ./ l') * l;   % alpha(i,j) = l(j) / l(i)
a = zeros(size(covar));
Mg = zeros(1,N);
Mg(1) = M(1);
a(:,1) = (l(1) * l .* covar(1,:))';     % a(i,1) = lambda(1)*lambda(i)*C(1,i)
for i = 2:N
    for j = 2:i
        s = 0;
        for k = 1: j-1
            s = s + a(i,k) * a(j,k) / Mg(k);
        end;
        a(i,j) = l(i) * l(j) * covar(i,j) - s;
        s = 0;
        for k = 1: i-1
            s = s + a(i,k);
        end;
        Mg(i) = M(i) - s;
    end;
end;
Pg = Mg * diag(1 ./ l);     % Pg(i) = Mg(i)./l(i)
g = zeros(n,N);
for j = 1:N;
    %   Each column of G contains samples of one variate.
    g(:,j) = gamrnd(Mg(j),Pg(j)/Mg(j),[n 1]);
end;
b = zeros(n,N,N);
s = zeros(n,1);
Gamma = zeros(n,N);
Gamma(:,1) = g(:,1);
for i = 2:N
    s = zeros(n,1);
    for j = 1:i-1
        %   b, Beta RVs container, is a 3D array with each (vertical) vector at
        % coordinations i,j (indicating length and width offset) contains samples
        % of a variate in its height. Note that b is computed for 1 <= j < i < N

        b(:,i,j) = betarnd(a(i,j),Mg(j)-a(i,j),[n 1]);  % b[ij] samples
        if j < i
            s = s + alpha(i,j) * b(:,i,j) .* g(:,j);
        end;
    end;
    Gamma(:,i) = g(:,i) + s;
end;
Na = sqrt(Gamma);

Hope it resolvoes your problem.

thank you
i will compare my code n see where i am going wrong. 
thanks again
Dhiraj