I need to generate a set of correlated random variables for a Monte Carlo simulation. The solutions I have found (http://www.stat.uiuc.edu/stat428/cndata.html, http://www.sitmo.com/doc/Generating_Correlated_Random_Numbers), using Cholesky Decomposition, seem to work only if the variables come from the same distribution with the same parameters. My situation is that each variable may be described by a different distribution (or different parameters of the same distribution). This approach does not seem to work, see code and results below. Am I missing something here? My math/statistics is not very good, will I need to generate correlated uniform random variables on (0,1) and then use the inverse distributions to get the desired results I am looking for? That is acceptable, but I would prefer to just generate the individual distributions and then correlate them. Any advice much appreciated. Thanks in advance
R. Males Cincinnati, Ohio, USA Sample Code: # Testing Correlated Random Variables # reference http://www.sitmo.com/doc/Generating_Correlated_Random_Numbers # reference http://www.stat.uiuc.edu/stat428/cndata.html # create the correlation matrix corMat=matrix(c(1,0.6,0.3,0.6,1,0.5,0.3,0.5,1),3,3) cholMat=chol(corMat) # create the matrix of random variables set.seed(1000) nValues=10000 # generate some random values matNormalAllSame=cbind(rnorm(nValues),rnorm(nValues),rnorm(nValues)) matNormalDifferent=cbind(rnorm(nValues,1,1.5),rnorm(nValues,2,0.5),rnorm(nValues,6,1.8)) matUniformAllSame=cbind(runif(nValues),runif(nValues),runif(nValues)) matUniformDifferent=cbind(runif(nValues,1,1.5),runif(nValues,2,3.5),runif(nValues,6,10.8)) # bind to a matrix print("correlation Matrix") print(corMat) print("Cholesky Decomposition") print (cholMat) # test same normal resultMatNormalAllSame=matNormalAllSame%*%cholMat print("correlation matNormalAllSame") print(cor(resultMatNormalAllSame)) # test different normal resultMatNormalDifferent=matNormalDifferent%*%cholMat print("correlation matNormalDifferent") print(cor(resultMatNormalDifferent)) # test same uniform resultMatUniformAllSame=matUniformAllSame%*%cholMat print("correlation matUniformAllSame") print(cor(resultMatUniformAllSame)) # test different uniform resultMatUniformDifferent=matUniformDifferent%*%cholMat print("correlation matUniformDifferent") print(cor(resultMatUniformDifferent)) and results [1] "correlation Matrix" [,1] [,2] [,3] [1,] 1.0 0.6 0.3 [2,] 0.6 1.0 0.5 [3,] 0.3 0.5 1.0 [1] "Cholesky Decomposition" [,1] [,2] [,3] [1,] 1 0.6 0.3000000 [2,] 0 0.8 0.4000000 [3,] 0 0.0 0.8660254 [1] "correlation matNormalAllSame" <== ok [,1] [,2] [,3] [1,] 1.0000000 0.6036468 0.3013823 [2,] 0.6036468 1.0000000 0.5005440 [3,] 0.3013823 0.5005440 1.0000000 [1] "correlation matNormalDifferent" <== no good [,1] [,2] [,3] [1,] 1.0000000 0.9141472 0.2676162 [2,] 0.9141472 1.0000000 0.2959178 [3,] 0.2676162 0.2959178 1.0000000 [1] "correlation matUniformAllSame" <== ok [,1] [,2] [,3] [1,] 1.0000000 0.5971519 0.2959195 [2,] 0.5971519 1.0000000 0.5011267 [3,] 0.2959195 0.5011267 1.0000000 [1] "correlation matUniformDifferent" <== no good [,1] [,2] [,3] [1,] 1.0000000 0.2312000 0.0351460 [2,] 0.2312000 1.0000000 0.1526293 [3,] 0.0351460 0.1526293 1.0000000 > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
