From: Maria Rizzo <mrizzo7_at_gmail.com>

Date: Thu, 17 Jul 2008 12:00:12 -0400

R-help_at_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. Received on Thu 17 Jul 2008 - 16:35:16 GMT

Date: Thu, 17 Jul 2008 12:00:12 -0400

See Chapter 22 in N.L. Johnson, S. Kotz, and N. Balakrishnan, "Continuous Univariate Distributions", Volume 2, Second Edition, 1995.

Maria

On Thu, Jul 17, 2008 at 11:29 AM, Mike Lawrence <Mike.Lawrence_at_dal.ca> wrote:

> Hi all,

*>
**> I'm looking for an analytic method to obtain the PDF & CDF of the sampling
**> distribution of a given correlation (rho) at a given sample size (N).
**>
**> I've attached code describing a monte carlo method of achieving this, and
**> while it is relatively fast, an analytic solution would obviously be
**> optimal.
**>
**> get.cors <- function(i, x, y, N){
**> end=i*N
**> .Internal(cor(x[(end-N+1):end] ,y[(end-N+1):end] ,TRUE ,FALSE ))
**> }
**> get.r.dist <- function(N, rho, it){
**> Sigma=matrix(c(1,rho,rho,1),2,2)
**> eS = eigen(Sigma, symmetric = TRUE, EISPACK = TRUE)
**> ev = eS$values
**> fact = eS$vectors %*% diag(sqrt(pmax(ev, 0)), 2)
**> Z = rnorm(2 * N * it)
**> dim(Z) = c(2, N * it)
**> Z = t(fact %*% Z)
**> x = Z[, 1]
**> y = Z[, 2]
**> r = sapply(1:it ,get.cors,x, y, N)
**> return(r)
**> }
**>
**> #Run 1e3 monte carlo iterations, where each obtains the correlation
**> # of 10 pairs of observations from a bivariate normal distribution with
**> # a true correlation of .5. Returns 1e3 values for the observed correlation
**> mc.rs = get.r.dist( N=10 , rho=.5 , it=1e3 )
**>
**> #plot the PDF & CDF
**> par(mfrow=c(1,2))
**> hist(mc.rs,prob=T,xlab='Observed correlation')
**> probs = seq(0,1,.01)
**> plot(quantile(mc.rs,probs=probs),probs,type='l',xlab='Observed
**> correlation',ylab='Cumulative probability')
**>
**> --
**> Mike Lawrence
**> Graduate Student, Department of Psychology, Dalhousie University
**>
**> www.memetic.ca
**>
**> "The road to wisdom? Well, it's plain and simple to express:
**> Err and err and err again, but less and less and less."
**> - Piet Hein
**>
**> ______________________________________________
**> R-help_at_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.
**>
*

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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. Received on Thu 17 Jul 2008 - 16:35:16 GMT

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