# [R] R: generating independent vectors

Chuck Cleland ccleland at optonline.net
Fri Mar 11 13:58:20 CET 2005

```You might try mvrnorm() in MASS.

library(MASS)
mvrnorm(n=10, mu=rep(0, 3), Sigma=diag(3), empirical=TRUE)

Clark Allan wrote:
> hi all
>
> i would like to generate independent vectors. i have included the code
> below. i display the correlation matrix of the n*p (n=the number of
> samples, p= the number of variables) matrix.
> what i find is that as n increases, the correlation matrix tends to an
> identity matrix. i.e. independence. for small samples (see examples
> below, for n=20, p=5 ; n=50,p=5, n=100,p=5; n=10000,p=5) the variables
> does not appear to be independent. note that i have not tested this
> statement statistically.
>
> ARE these variables independent? by setting the seed for each variable
> run i HOPE that the variables are now independent. IS this true??? if
> not does anyone know how to generate these independent variables?
>
> how does R generate its random variables? does it use the box muller
> technique? if so how does it generate the random uniform variables?
>
> ***
> allan
>
>
>
> IND<-function(rows.=10,col.=3)
> {
> a<-matrix(nrow=rows.,ncol=col.)
> for (j in 1:col.)
> {
> 	set.seed(j)
> 	r<-rnorm(rows.)
> 	a[,j]<-r
> }
> #list(a=a,cor=cor(a))
> cor(a)
> }
> IND(rows.=10,col.=3)
>
>
>
>
>>IND(rows.=20,col.=5)
>
>             [,1]        [,2]        [,3]        [,4]       [,5]
> [1,]  1.00000000  0.25677165 -0.14882130 -0.09190797  0.1562481
> [2,]  0.25677165  1.00000000  0.02585515  0.13735712 -0.1443301
> [3,] -0.14882130  0.02585515  1.00000000 -0.11311416  0.1437001
> [4,] -0.09190797  0.13735712 -0.11311416  1.00000000  0.1833647
> [5,]  0.15624807 -0.14433011  0.14370006  0.18336467  1.0000000
>
>
>
>>IND(rows.=50,col.=5)
>
>               [,1]        [,2]          [,3]        [,4]        [,5]
> [1,]  1.0000000000  0.07915025  0.0009239851 -0.14102117 -0.07335342
> [2,]  0.0791502463  1.00000000 -0.1764530631  0.10021081  0.19742285
> [3,]  0.0009239851 -0.17645306  1.0000000000  0.02968062  0.14543350
> [4,] -0.1410211698  0.10021081  0.0296806188  1.00000000  0.07234953
> [5,] -0.0733534183  0.19742285  0.1454335014  0.07234953  1.00000000
>
>
>>IND(rows.=100,col.=5)
>
>             [,1]       [,2]         [,3]         [,4]       [,5]
> [1,]  1.00000000 -0.1537208 -0.023741715 -0.135245915 0.01961224
> [2,] -0.15372076  1.0000000 -0.141796984  0.157219334 0.15518443
> [3,] -0.02374171 -0.1417970  1.000000000  0.005865698 0.19118563
> [4,] -0.13524592  0.1572193  0.005865698  1.000000000 0.07345299
> [5,]  0.01961224  0.1551844  0.191185627  0.073452993 1.00000000
>
>
>>IND(rows.=10000,col.=5)
>
>              [,1]         [,2]         [,3]         [,4]         [,5]
> [1,]  1.000000000  0.015928444 -0.008288940 -0.005646904  0.006936662
> [2,]  0.015928444  1.000000000 -0.005444611  0.005242395 -0.008246009
> [3,] -0.008288940 -0.005444611  1.000000000  0.007277489  0.012299247
> [4,] -0.005646904  0.005242395  0.007277489  1.000000000  0.001918704
> [5,]  0.006936662 -0.008246009  0.012299247  0.001918704  1.000000000
>
>
> ------------------------------------------------------------------------
>
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--
Chuck Cleland, Ph.D.
NDRI, Inc.
71 West 23rd Street, 8th floor
New York, NY 10010
tel: (212) 845-4495 (Tu, Th)
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fax: (917) 438-0894

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