random

Random variate from Gaussian mixture distribution

Syntax

Y = random(gm)

Y = random(gm,n)

[Y,compIdx] = random(___)

Description

Y = random(gm) generates a 1-by-m random variate from the m-dimensional Gaussian mixture distribution gm.

Y = random(gm,n) returns n random variates. Each row of Y is a random variate generated from the m-dimensional Gaussian mixture distribution gm.

[Y,compIdx] = random(___) also returns an n-by-1 index vector compIdx for any of the input arguments in previous syntaxes. compIdx(i) indicates the mixture component used to generate the ith random variate Y(i,:).

Examples

Generate Random Variates

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 Random Number Generator

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

Input Arguments

gm — Gaussian mixture distribution

gmdistribution object

Gaussian mixture distribution, also called Gaussian mixture model (GMM), specified as a gmdistribution object.

You can create a gmdistribution object using gmdistribution or fitgmdist. Use the gmdistribution function to create a gmdistribution object by specifying the distribution parameters. Use the fitgmdist function to fit a gmdistribution model to data given a fixed number of components.

n — Number of random variates

1 (default) | positive integer

Number of random variates to generate, specified as a positive integer.

Data Types: single | double

Output Arguments

Y — Random variate

1-by-m numeric vector | n-by-m numeric matrix

Random variate, returned as a 1-by-m numeric vector or an n-by-m numeric matrix. Each row of Y is a random variate generated from the m-dimensional Gaussian mixture distribution gm.

compIdx — Component index

positive integer | n-by-1 numeric vector

Component index, returned as a positive integer or an n-by-1 index vector, where compIdx(i) indicates the mixture component used to generate the ith random variate Y(i,:).