random

Create a gmdistribution object and generate random variates.

Define the distribution parameters (means and covariances) of a two-component bivariate Gaussian mixture distribution.

mu = [1 2;-3 -5];
sigma = [1 1]; % shared diagonal covariance matrix

Create a gmdistribution object by using the gmdistribution function. By default, the function creates an equal proportion mixture.

gm = gmdistribution(mu,sigma)

gm = 

Gaussian mixture distribution with 2 components in 2 dimensions
Component 1:
Mixing proportion: 0.500000
Mean:     1     2

Component 2:
Mixing proportion: 0.500000
Mean:    -3    -5

Generate 1000 random variates.

rng('default'); % For reproducibility
[Y,compIdx] = random(gm,1000);

compIdx(i) indicates the mixture component used to generate the ith random variate Y(i,:). Count the number of random variates generated by Component 1.

numIdx1 = sum(compIdx == 1)

numIdx1 = 
512

random generates about half of the random variates using Component 1 because gm has equal mixing proportions.

Plot the generated random variates by using scatter.

scatter(Y(:,1),Y(:,2),10,'.') % Scatter plot with points of size 10

Reset the random number generator to generate the same random variate.

Define the distribution parameters (means, covariances, and mixing proportions) of two bivariate Gaussian mixture components.

p = [0.4 0.6];               % Mixing proportions     
mu = [1 2;-3 -5];            % Means
sigma = cat(3,[2 .5],[1 1])  % Covariances 1-by-2-by-2 array

sigma = 
sigma(:,:,1) =

    2.0000    0.5000


sigma(:,:,2) =

     1     1

The cat function concatenates the covariances along the third array dimension. The defined covariance matrices are diagonal matrices. sigma(1,:,i) contains the diagonal elements of the covariance matrix of component i.

Create a gmdistribution object by using the gmdistribution function.

gm = gmdistribution(mu,sigma);

Save the current state of the random number generator, and then generate a random variate using gm.

s = rng;
r = random(gm)

r = 1×2

   -1.1661   -7.2588

Restore the state of the random number generator to s, and then generate a random variate using gm. The values are the same as before.

rng(s);
r1 = random(gm)

r1 = 1×2

   -1.1661   -7.2588