Re: [R] Generating correlated data from uniform distribution
Here is an approach using 'optim' and simulated annealing:
x - sort(runif(1000))
y - sort(runif(1000))
ord - 1:1000
target - function(ord){ ( cor(x, y[ord]) - 0.6 ) ^2 }
new.point - function(ord){
tmp - sample(length(ord), 2)
ord[tmp] - ord[rev(tmp)]
ord
}
new.point2 - function(ord){
tmp - sample(length(ord) -100, 1)
tmp2 - sample(100, 1)
ord[ c(tmp, tmp+tmp2) ] - ord[ c(tmp+tmp2, tmp) ]
ord
}
res - optim(ord, target, new.point, method=SANN,
control = list(maxit=6000, temp=2000, trace=TRUE))
res2 - optim(ord, target, new.point2, method=SANN,
control = list(maxit=6, temp=200, trace=TRUE))
y - y[res$par]
par(mfrow=c(2,2))
hist(x)
hist(y)
plot(x,y)
cor(x,y)
y - sort(y)[res2$par]
par(mfrow=c(2,2))
hist(x)
hist(y)
plot(x,y)
cor(x,y)
Hope this helps,
Greg Snow, Ph.D.
Statistical Data Center, LDS Hospital
Intermountain Health Care
[EMAIL PROTECTED]
(801) 408-8111
Jim Brennan [EMAIL PROTECTED] 07/01/05 05:25PM
OK now I am skeptical especially when you say in a weird way:-)
This may be OK but look at plot(x,y) and I am suspicious. Is it still
alright with this kind of relationship?
For large N it appears Spencer's method is returning slightly lower
correlation for the uniforms as compared to the normals so maybe there is a
problem!?!
Hope we are all learning something and Menghui gets/has what he wants . :-)
-Original Message-
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Peter
Dalgaard
Sent: July 1, 2005 6:59 PM
To: Jim Brennan
Cc: 'Tony Plate'; 'Menghui Chen'; r-help@stat.math.ethz.ch
Subject: Re: [R] Generating correlated data from uniform distribution
Jim Brennan [EMAIL PROTECTED] writes:
Yes you are right I guess this works only for normal data. Free advice
sometimes comes with too little consideration :-)
Worth every cent...
Sorry about that and thanks to Spencer for the correct way.
Hmm, but is it? Or rather, what is the relation between the
correlation of the normals and that of the transformed variables?
Looks nontrivial to me.
Incidentally, here's a way that satisfies the criteria, but in a
rather weird way:
N - 1
rho - .6
x - runif(N, -.5,.5)
y - x * sample(c(1,-1), N, replace=T, prob=c((1+rho)/2,(1-rho)/2))
--
O__ Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907
__
R-help@stat.math.ethz.ch mailing list
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[R] Generating correlated data from uniform distribution
While you are looking at weird distributions, here is one that we have used in experiments on noise masking to explore the bandwidth of visual mechanisms D'Zmura, M., Knoblauch, K. (1998). Spectral bandwidths for the detection of color. Vision Research, 20, 3117-28 and G. Monaci, G. Menegaz, S. Susstrunk and K. Knoblauch Chromatic Contrast Detection in Spatial Chromatic Noise Visual Neuroscience, Vol. 21, No 3, pp. 291-294, 2004 N - 1 x - runif(N, -.5,.5) y - runif(N, -abs(x), abs(x)) plot(x,y) y is not uniform but it is conditional on x. The plot reveals why we called this sectored noise. HTH ken Jim Brennan jfbrennan at rogers.com writes: Yes you are right I guess this works only for normal data. Free advice sometimes comes with too little consideration :-) Worth every cent... Sorry about that and thanks to Spencer for the correct way. Hmm, but is it? Or rather, what is the relation between the correlation of the normals and that of the transformed variables? Looks nontrivial to me. Incidentally, here's a way that satisfies the criteria, but in a rather weird way: N - 1 rho - .6 x - runif(N, -.5,.5) y - x * sample(c(1,-1), N, replace=T, prob=c((1+rho)/2,(1-rho)/2)) -- O__ Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907 Ken Knoblauch Inserm U371, Cerveau et Vision Department of Cognitive Neurosciences 18 avenue du Doyen Lepine 69500 Bron France tel: +33 (0)4 72 91 34 77 fax: +33 (0)4 72 91 34 61 portable: 06 84 10 64 10 http://www.lyon.inserm.fr/371/ __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Generating correlated data from uniform distribution
Jim Brennan [EMAIL PROTECTED] writes: OK now I am skeptical especially when you say in a weird way:-) This may be OK but look at plot(x,y) and I am suspicious. Is it still alright with this kind of relationship? ... N - 1 rho - .6 x - runif(N, -.5,.5) y - x * sample(c(1,-1), N, replace=T, prob=c((1+rho)/2,(1-rho)/2)) Well, the covariance is (everything has mean zero, of course) E(XY) = (1+rho)/2*EX^2 + (1-rho)/2*E(X*-X) = rho*EX^2 The marginal distribution of Y is a mixture of two identical uniforms (X and -X) so is uniform and in particular has the same variance as X. In summary, EXY/sqrt(EX^2EY^2) == rho So as I said, it satisfies the formal requirements. X and Y are uniformly distributed and their correlation is rho. If for nothing else, I suppose that this example is good for demonstrating that independence and uncorrelatedness is not the same thing. -- O__ Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Generating correlated data from uniform distribution
On 02-Jul-05 Peter Dalgaard wrote: Jim Brennan [EMAIL PROTECTED] writes: OK now I am skeptical especially when you say in a weird way:-) This may be OK but look at plot(x,y) and I am suspicious. Is it still alright with this kind of relationship? ... N - 1 rho - .6 x - runif(N, -.5,.5) y - x * sample(c(1,-1), N, replace=T, prob=c((1+rho)/2,(1-rho)/2)) Well, the covariance is (everything has mean zero, of course) E(XY) = (1+rho)/2*EX^2 + (1-rho)/2*E(X*-X) = rho*EX^2 The marginal distribution of Y is a mixture of two identical uniforms (X and -X) so is uniform and in particular has the same variance as X. In summary, EXY/sqrt(EX^2EY^2) == rho So as I said, it satisfies the formal requirements. X and Y are uniformly distributed and their correlation is rho. If for nothing else, I suppose that this example is good for demonstrating that independence and uncorrelatedness is not the same thing. That was a nice sneaky solution! I was toying with something similar, but less sneaky, until I saw Peter's, on the lines of x-runif(2N, -0.5,0.5); ix-(N-k):(N+k); y-x; y[ix]-(-y[ix]) (which makes the same point about independence and correlation). The larger k as a fraction of N, the more you swing from rho = 1 to rho = -1, but you cannot achieve, as Peter did, an arbitrary correlation coefficient rho since the value depends on k which can only take discrete values. Another approach which leads to a less special joint distribution is x-sort(runif(N, -0.5,0.5)); y-sort(runif(N, -0.5,0.5)) followed by a rho-dependent permutation of y. I'm still pondering a way of choosing the permutation so as to get a desired rho. The extremes are the identity, which for a given sample will give as close as you can get to rho = +1, and reversal, which gives as close as you can get to rho = -1. However, the maximum theoretical rho which you can get (as opposed to what is possible for particular samples, which may get arbitrarily close to +1) depends on N. For instance, with N=3, it looks as though the theoretical rho is about 0.9 with the identity permutation (for N=1000, however, just about all samples give rho 0.99). I smell a source of interesting exam questions ... Over to you! Best wishes, Ted. E-Mail: (Ted Harding) [EMAIL PROTECTED] Fax-to-email: +44 (0)870 094 0861 Date: 02-Jul-05 Time: 12:22:09 -- XFMail -- __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
[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 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Generating correlated data from uniform distribution
dat-matrix(runif(2000),2,1000) rho-.77 R-matrix(c(1,rho,rho,1),2,2) dat2-t(ch)%*%dat cor(dat2[1,],dat2[2,]) [1] 0.7513892 dat-matrix(runif(2),2,1) 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(20),2,10) 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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] 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 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Generating correlated data from uniform distribution
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 0.16418 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(2),2,1) 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(20),2,10) 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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] 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 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Generating correlated data from uniform distribution
How about tetrachoric correlations? Generate correlated normal observations, then convert to uniform using pnorm: rho - 0.9 Cor - array(c(1, rho, rho, 1), dim=c(2,2)) library(mvtnorm) set.seed(1) Y - rmvnorm(1, sigma=Cor) X - pnorm(Y)-0.5 plot(X) hist(X[,1]) hist(X[,2]) cor(X) Enjoy. spencer graves Tony Plate wrote: 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 0.16418 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(2),2,1) 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(20),2,10) 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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] 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 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html -- Spencer Graves, PhD Senior Development Engineer PDF Solutions, Inc. 333 West San Carlos Street Suite 700 San Jose, CA 95110, USA [EMAIL PROTECTED] www.pdf.com http://www.pdf.com Tel: 408-938-4420 Fax: 408-280-7915 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Generating correlated data from uniform distribution
Yes you are right I guess this works only for normal data. Free advice sometimes comes with too little consideration :-) Sorry about that and thanks to Spencer for the correct way. -Original Message- From: Tony Plate [mailto:[EMAIL PROTECTED] Sent: July 1, 2005 6:01 PM To: Jim Brennan Cc: 'Menghui Chen'; r-help@stat.math.ethz.ch Subject: Re: [R] Generating correlated data from uniform distribution 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 0.16418 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(2),2,1) 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(20),2,10) 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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] 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 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Generating correlated data from uniform distribution
Jim Brennan [EMAIL PROTECTED] writes: Yes you are right I guess this works only for normal data. Free advice sometimes comes with too little consideration :-) Worth every cent... Sorry about that and thanks to Spencer for the correct way. Hmm, but is it? Or rather, what is the relation between the correlation of the normals and that of the transformed variables? Looks nontrivial to me. Incidentally, here's a way that satisfies the criteria, but in a rather weird way: N - 1 rho - .6 x - runif(N, -.5,.5) y - x * sample(c(1,-1), N, replace=T, prob=c((1+rho)/2,(1-rho)/2)) -- O__ Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Generating correlated data from uniform distribution
OK now I am skeptical especially when you say in a weird way:-) This may be OK but look at plot(x,y) and I am suspicious. Is it still alright with this kind of relationship? For large N it appears Spencer's method is returning slightly lower correlation for the uniforms as compared to the normals so maybe there is a problem!?! Hope we are all learning something and Menghui gets/has what he wants . :-) -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Peter Dalgaard Sent: July 1, 2005 6:59 PM To: Jim Brennan Cc: 'Tony Plate'; 'Menghui Chen'; r-help@stat.math.ethz.ch Subject: Re: [R] Generating correlated data from uniform distribution Jim Brennan [EMAIL PROTECTED] writes: Yes you are right I guess this works only for normal data. Free advice sometimes comes with too little consideration :-) Worth every cent... Sorry about that and thanks to Spencer for the correct way. Hmm, but is it? Or rather, what is the relation between the correlation of the normals and that of the transformed variables? Looks nontrivial to me. Incidentally, here's a way that satisfies the criteria, but in a rather weird way: N - 1 rho - .6 x - runif(N, -.5,.5) y - x * sample(c(1,-1), N, replace=T, prob=c((1+rho)/2,(1-rho)/2)) -- O__ Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Generating correlated data from uniform distribution
Peter is absolutely correct: The correlation I used was for a hidden normal process, not for the resultant correlated uniforms. This is similar to but different from tetrachoric corrrelations, about which there is a substantial literature (including an R package polycor). Why do you want correlated uniforms? What do they represent physically? Does it matter if you can match exactly a particular correlation coefficient, or is it enough to say that they are uniformily distributed random variables such that their normal scores have a specified correlation coefficient? There is so much known about the multivariate normal distribution and so little about correlated uniforms that it might be more useful to know the correlations of latent normals, for which your uniforms are what are measured. spencer graves Peter Dalgaard wrote: Jim Brennan [EMAIL PROTECTED] writes: Yes you are right I guess this works only for normal data. Free advice sometimes comes with too little consideration :-) Worth every cent... Sorry about that and thanks to Spencer for the correct way. Hmm, but is it? Or rather, what is the relation between the correlation of the normals and that of the transformed variables? Looks nontrivial to me. Incidentally, here's a way that satisfies the criteria, but in a rather weird way: N - 1 rho - .6 x - runif(N, -.5,.5) y - x * sample(c(1,-1), N, replace=T, prob=c((1+rho)/2,(1-rho)/2)) -- Spencer Graves, PhD Senior Development Engineer PDF Solutions, Inc. 333 West San Carlos Street Suite 700 San Jose, CA 95110, USA [EMAIL PROTECTED] www.pdf.com http://www.pdf.com Tel: 408-938-4420 Fax: 408-280-7915 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Generating correlated data from uniform distribution
Dear Menghui, You may consider looking in Luc Devroye's Non-uniform Random Number Generation. Despite its title, section XI.3.2 describes how to generate bivariate uniforms. The book is out of print but Devroye himself urges you to print it from his scanned PDFs(!): http://cgm.cs.mcgill.ca/~luc/rnbookindex.html Hope this helps, alejandro On 7/1/05, Menghui Chen [EMAIL PROTECTED] wrote: 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 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
