Matlab Error: Index in Position 1 exceeds array bounds

Question

I am attempting to create a gamma distribution in MATLAB; however, I keep receiving the error:

Index in Position 1 exceeds array bounds (must not exceed 100).

Assuming I am reading this correctly, it is referring to variable M that is simply = 2500 (the number of pseudo-random variables I am using for this project).

I was hoping someone can explain what is wrong with my logic and possibly a solution.

alpha = 0.5;
w = gamma_rdn(M,alpha);
x1 = (0.0001:0.001:1); % For plot

figure(5)
subplot(2,1,1);hist(w);title('Histogram of Gamma RDN');
subplot(2,1,2);plot(x1,pdf('gam',x1,alpha,1));title('Theoretical Gamma Density with \alpha = 0.5');
axis([0 1 0 100]);

% The gamma_rdn function is implemented as follows:
function[w] = gamma_rdn(M,alpha)
    % Generate random numbers from the gamma distribution with parameter
    % alpha <= 1, beta = 1
    pe = exp(1);
    w = zeros(M,1);
    u = rand(100,1);
    b = (alpha + pe)/pe;
    i = 0;
    j = 0;
    while j < M
        i = i+1;
        y = b*u(i,1);
        if y <= 1
            z = y^(1/alpha);
            i = i+1;
            if u(i,1) <= exp(-z)
                j = j+1;
                w(j,1) = z;
            else
                i = i+1;
            end
        else
            z = -log((b-y)/alpha);
            i = i+1;
            if u(i,1) <= z^(alpha - 1)
                j = j+1;
                w(j,1) = z;
            else
                i = i+1;
            end
        end
    end
    if i > 95
        u = rand(100,1);
        i = 0;
    end
end

Answer 1

Is there a particular reason you chose u = rand(100,1)?

The problem is coming because in while loop, as soon as variable i exceeds 100 (say i=101), y = b*u(i,1) becomes invalid. That is, you are trying to access u(101,1) while the size of u is (100,1).

If there's not particular reason, try a large enough size, like, u = rand(10000,1).