dcor0 {GeneTS} | R Documentation |
Density and distribution function and a random number generator
of Pearson's correlation coefficient assuming that there is no
correlation present (rho = 0
).
The distribution has a single parameter, namely the degree of freedom kappa
which
equals 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 investigated variables. If a simple correlation coefficient is considered (p=2)
then the degree of freedom equals kappa = n-1
.
For p variables and a partial correlation coefficient conditioned on p-2 variables
kappa = n-p+1
.
The incomplete beta function ibeta
is needed to compute the distribution function. For
z=1 the incomplete beta function reduces to the beta function
(i.e. ibeta(1, a, b) = beta(a, b)
).
dcor0(x, kappa, log=FALSE) pcor0(q, kappa, lower.tail=TRUE, log.p=FALSE) rcor0(n, kappa) ibeta(z, a, b)
x,q |
vector of sample correlations |
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] |
a,b,z |
numeric vectors |
For density and distribution functions (as well as a corresponding random number generator)
of the correlation coefficient for arbitrary values of rho please refer to the
SuppDists
package by Bob Wheeler bwheeler@echip.com (available on CRAN).
Note that the parameter N in the dPearson
function (and others in the SuppDists
package)
corresponds to N=kappa+1
.
The output values conform to the output from other such functions
in R. dcor0
gives the density and pcor0
the distribution function.
The function ibeta
returns a numeric value.
Korbinian Strimmer (http://www.statistik.lmu.de/~strimmer/).
# load GeneTS library library("GeneTS") # 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) # incomplete beta function ibeta(0.4, 1, 3) ibeta(1, 2, 3) beta(2, 3)