# Re: [R] Generating correlated data from uniform distribution

From: Tony Plate <tplate_at_acm.org>
Date: Sat 02 Jul 2005 - 08:00:51 EST

Isn't this a little trickier with non-normal variables? It sounds like Menghui Chen wants variables that have uniform marginal distribution, and a specified correlation.

When I look at histograms (or just the quantiles) of the rows of dat2 in your example, I see something for dat2[2,] that does not look much like it comes from a uniform distribution.

``` > dat<-matrix(runif(2000),2,1000)
> rho<-.77
> R<-matrix(c(1,rho,rho,1),2,2)
> ch<-chol(R)
> dat2<-t(ch)%*%dat
> cor(dat2[1,],dat2[2,])
```

[1] 0.7513892
``` > hist(dat2[1,])
> hist(dat2[2,])
>
> quantile(dat2[1,])
0%         25%         50%         75%        100%
```
0.000655829 0.246216035 0.507075912 0.745158441 0.999916418  > quantile(dat2[2,])

0% 25% 50% 75% 100% 0.0393046 0.4980066 0.7150426 0.9208855 1.3864704  >

• Tony Plate

Jim Brennan wrote:
> dat<-matrix(runif(2000),2,1000)
> rho<-.77
> R<-matrix(c(1,rho,rho,1),2,2)
> ch<-chol(R)
> dat2<-t(ch)%*%dat
> cor(dat2[1,],dat2[2,])
[1] 0.7513892
>

```>>dat<-matrix(runif(20000),2,10000)
>>rho<-.28
>>R<-matrix(c(1,rho,rho,1),2,2)
>>ch<-chol(R)
>>dat2<-t(ch)%*%dat
>>cor(dat2[1,],dat2[2,])
```

>
> [1] 0.2681669
>
```>>dat<-matrix(runif(200000),2,100000)
>>rho<-.28
>>R<-matrix(c(1,rho,rho,1),2,2)
>>ch<-chol(R)
>>dat2<-t(ch)%*%dat
>>cor(dat2[1,],dat2[2,])
```

>
> [1] 0.2814035
>
> See ?choleski
>
> -----Original Message-----
> From: r-help-bounces@stat.math.ethz.ch
> [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Menghui Chen
> Sent: July 1, 2005 4:49 PM
> To: r-help@stat.math.ethz.ch
> Subject: [R] Generating correlated data from uniform distribution
>
> Dear R users,
>
> I want to generate two random variables (X1, X2) from uniform
> distribution (-0.5, 0.5) with a specified correlation coefficient r.
> Does anyone know how to do it in R?
>
> Many thanks!
>
> Menghui
>
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