dcor0 {GeneTS} R Documentation

## Distribution of the Vanishing Correlation Coefficient (rho=0) and Related Functions

### Description

Density and distribution function and a random number generator of Pearson's correlation coefficient assuming that there is no correlation present (rho = 0).

The degree of freedom kappa depends both on the sample size N and the number G of investigated variables, i.e. whether simple or partial correlation coefficients are being considered. For G=2 (simple correlation coefficient) the degree of freedom equals kappa = N-1, whereas for arbitrary G (with G-2 variables eliminated in the partial correlation coefficient) kappa = N-G+1 (see also `cor0.estimate.kappa`).

The incomplete beta function is needed to compute the distribution function. For z=1 the incomplete beta function reduces to the beta function (`ibeta`(1, a, b) = `beta`(a, b)).

### Usage

```dcor0(x, kappa, log=FALSE)
pcor0(q, kappa, lower.tail=TRUE, log.p=FALSE)
rcor0(n, kappa)
ibeta(z, a, b)
```

### Arguments

 `x,q` vector of sample correlations `kappa` the degree of freedom of the distribution `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

### Details

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 (i.e. G=2).

### Value

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.

### Author(s)

Juliane Schaefer (http://www.stat.uni-muenchen.de/~schaefer/) and Korbinian Strimmer (http://www.stat.uni-muenchen.de/~strimmer/).

`cor`, `cor0.estimate.kappa`, `beta`.

### Examples

```# 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)
```

[Package GeneTS version 2.3 Index]