Distribution of the Vanishing Correlation Coefficient (rho=0) and Related Functions
The above functions describe the distribution of the Pearson correlation
coefficient r assuming that there is no correlation present (rho = 0).
Note that the distribution has only a single parameter: the degree
of freedom kappa, which is equal to the inverse of the variance of the distribution.
The theoretical value of kappa depends both on the sample size n and the number
p of considered variables. If a simple correlation coefficient between two
variables (p=2) is considered the degree of freedom equals kappa = n-1.
However, if a partial correlation coefficient is considered (conditioned on p-2 remaining
variables) the degree of freedom is kappa = n-1-(p-2) = n-p+1.
dcor0(x, kappa, log=FALSE) pcor0(q, kappa, lower.tail=TRUE, log.p=FALSE) qcor0(p, kappa, lower.tail=TRUE, log.p=FALSE) rcor0(n, kappa)
x,q |
vector of sample correlations |
p |
vector of probabilities |
kappa |
the degree of freedom of the distribution (= inverse variance) |
n |
number of values to generate. If n is a vector, length(n) values will be generated |
log, log.p |
logical vector; if TRUE, probabilities p are given as log(p) |
lower.tail |
logical vector; if TRUE (default), probabilities are P[R <= r], otherwise, P[R > r] |
For density and distribution functions as well as a corresponding random number generator
of the correlation coefficient for arbitrary non-vanishing correlation rho please refer to the
SuppDists package by Bob Wheeler bwheeler@echip.com (available on CRAN).
Note that the parameter N in his dPearson function corresponds to N=kappa+1.
dcor0 gives the density, pcor0
gives the distribution function, qcor0 gives
the quantile function, and rcor0 generates random deviates.
Korbinian Strimmer (http://www.strimmerlab.org).
cor.
# load fdrtool library
library("fdrtool")
# distribution of r for various degrees of freedom
x = seq(-1,1,0.01)
y1 = dcor0(x, kappa=7)
y2 = dcor0(x, kappa=15)
plot(x,y2,type="l", xlab="r", ylab="pdf",
xlim=c(-1,1), ylim=c(0,2))
lines(x,y1)
# simulated data
r = rcor0(1000, kappa=7)
hist(r, freq=FALSE,
xlim=c(-1,1), ylim=c(0,5))
lines(x,y1,type="l")
# distribution function
pcor0(-0.2, kappa=15)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.