How to generate random numbers in mixture normal distribution (considering weight)?

For a mixture normal distribution the code below is used (for 1000 sample):

x1= mu(1) + std(1)*randn(1000,1)

x2= mu(2) + std(2)*randn(1000,1)

But, I wan to take the respected weight into account, Wi=[0.8 0.2], for instance.

I tried this code, but when I plot the PDFs of them, it gives me wrong curves.

x1= Wi(1)*(mu(1) + std(1)*randn(1000,1));

x2= Wi(2)*(mu(2) + std(2)*randn(1000,1));

I was wondering how I can solve this problem?

Answer 1

[the cyclist]

Does this do what you intend?

mu  = [0 5];
std = [1 1];

N = 1000;

r = rand(N,1);

x1= (r >0.8).*(mu(1) + std(1)*randn(N,1));
x2= (r<=0.8).*(mu(2) + std(2)*randn(N,1));

x = x1+x2;

figure
histogram(x,99)

[Amin Ganjavi]

Thanks for your reply.

What if I have more than two weight, for example 4 different data.

Wi=[0.1 0.2 0.4 0.3]

Thanks

[the cyclist]

mu  = [0 3 6 9];
std = [1 1 1 1];

W = [0.1 0.2 0.3 0.4]; % Make sure to normalize this, if it isn't already
cumW = [0 cumsum(W)];

N = 100000;

r = rand(N,1);

xsum = zeros(N,1);

for k = 1:numel(mu)
    x{k} = (r > cumW(k) & r <= cumW(k+1)).*(mu(k) + std(k)*randn(N,1));
    xsum = xsum + x{k};
end

figure
histogram(xsum,99)

[Amin Gan]

Thank you very much