R: Distribution of the Vanishing Correlation Coefficient (rho=0)...
dcor0
R Documentation
Distribution of the Vanishing Correlation Coefficient (rho=0) and Related Functions
Description
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.
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]
Details
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.
Value
dcor0 gives the density, pcor0
gives the distribution function, qcor0 gives
the quantile function, and rcor0 generates random deviates.
# 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)