How to insert correlation co-efficient matrix between variables following normal distribution in matlab?

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Abhishek 2014-8-19

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评论： Abhishek 2014-8-20

Let, there be two variables, amax, maximum value of horizontal ground acceleration and mw, magnitude of an earthquake required to find out CSR, cyclic stress ratio, a term related to liquefaction. Both of these variables follow normal random distribution and the correlation coefficient between them is 0.9. I have defined the two concerned variables as uncorrelated ones in the following manner,

amax=normrnd(mean,standard deviation,no. of rows,no. of columns); mw=normrnd(mean,standard deviation,no. of rows,no. of columns);

normrnd is a command in the matlab to generate a normal distribution of given size, for a particular value of mean and standard deviation.

For each of these values I found out corresponding CSR values through an empirical formula. Suggest me how to insert the correlation co-efficient matrix(symmetric) of order 2x2 in a matlab program along with the definitions of these two variables.

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Answer 1

Aniruddha Katre 2014-8-19

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在 MATLAB Online 中打开

It seems like you want to generate two normally distributed random variables with correlation of 0.9. You can use the function "mvnrnd" from the statistics toolbox.

mu = [2 3]; % Vector of means. mean of amax is 2 and mean of mw is 3
sig = [1 0.9;0.9 1]; % Covariance matrix. Correlation is 0.9
nPts = 50; % Number of points you want to generate for each random variable
rVec = mvnrnd(mu,sig,nPts); % Generate the correlated random variables

Documentation for "mvnrnd": http://www.mathworks.com/help/stats/mvnrnd.html

Then you can extract "amax" and "mw" from "rVec":