(13 votes, average: 3.31 out of 5)This article discusses the method of generating two correlated random sequences using Matlab. If you are looking for the method on generating multiple sequences of correlated random numbers, I urge you to go here.
Generating two vectors of correlated random numbers, given the correlation coefficient 
, is implemented in two steps. The first step is to generate two uncorrelated random sequences from an underlying distribution. Normally distributed random sequences are considered here.
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Step 1: Generate two uncorrelated Gaussian distributed random sequences 
x1=randn(1,100); %Normal random numbers sequence 1
x2=randn(1,100); %Normal random numbers sequence 2
subplot(1,2,1); plot(x1,x2,'r*');
title('Uncorrelated RVs X_1 and X_2');
xlabel('X_1'); ylabel('X_2');Step 2: Generate correlated random sequence z
In the second step, the required correlated sequence is generated as
rho=0.9;
z=rho*x1+sqrt(1-rhoˆ2)*x2;%transformation
subplot(1,2,2); plot(x1,z,'r*');
title(['Correlated RVs X_1 and Z , \rho=',num2str(rho)]);
xlabel('X_1'); ylabel('Z');The resulting sequence Z will have correlation with respect to 
Results plotted below.
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Further reading
Topics in this chapter
| Random Variables - Simulating Probabilistic Systems ● Introduction ● Plotting the estimated PDF ● Univariate random variables □ Uniform random variable □ Bernoulli random variable □ Binomial random variable □ Exponential random variable □ Poisson process □ Gaussian random variable □ Chi-squared random variable □ Non-central Chi-Squared random variable □ Chi distributed random variable □ Rayleigh random variable □ Ricean random variable □ Nakagami-m distributed random variable ● Central limit theorem - a demonstration ● Generating correlated random variables □ Generating two sequences of correlated random variables □ Generating multiple sequences of correlated random variables using Cholesky decomposition ● Generating correlated Gaussian sequences □ Spectral factorization method □ Auto-Regressive (AR) model |
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