Description Usage Arguments Details Value Author(s) See Also Examples

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`

.

1 2 3 4 |

`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 |

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 (https://strimmerlab.github.io).

`cor`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
# 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)
``` |

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