SignRank {stats} | R Documentation |

## Distribution of the Wilcoxon Signed Rank Statistic

### Description

Density, distribution function, quantile function and random
generation for the distribution of the Wilcoxon Signed Rank statistic
obtained from a sample with size `n`

.

### Usage

dsignrank(x, n, log = FALSE)
psignrank(q, n, lower.tail = TRUE, log.p = FALSE)
qsignrank(p, n, lower.tail = TRUE, log.p = FALSE)
rsignrank(nn, n)

### Arguments

`x,q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`nn` |
number of observations. If `length(nn) > 1` , the length
is taken to be the number required. |

`n` |
number(s) of observations in the sample(s). A positive
integer, or a vector of such integers. |

`log, log.p` |
logical; if TRUE, probabilities p are given as log(p). |

`lower.tail` |
logical; if TRUE (default), probabilities are
*P[X <= x]*, otherwise, *P[X > x]*. |

### Details

This distribution is obtained as follows. Let `x`

be a sample of
size `n`

from a continuous distribution symmetric about the
origin. Then the Wilcoxon signed rank statistic is the sum of the
ranks of the absolute values `x[i]`

for which `x[i]`

is
positive. This statistic takes values between *0* and
*n(n+1)/2*, and its mean and variance are *n(n+1)/4* and
*n(n+1)(2n+1)/24*, respectively.

If either of the first two arguments is a vector, the recycling rule is
used to do the calculations for all combinations of the two up to
the length of the longer vector.

### Value

`dsignrank`

gives the density,
`psignrank`

gives the distribution function,
`qsignrank`

gives the quantile function, and
`rsignrank`

generates random deviates.

### Author(s)

Kurt Hornik

### See Also

`wilcox.test`

to calculate the statistic from data, find p
values and so on.

`dwilcox`

etc, for the distribution of *two-sample*
Wilcoxon rank sum statistic.

### Examples

par(mfrow=c(2,2))
for(n in c(4:5,10,40)) {
x <- seq(0, n*(n+1)/2, length=501)
plot(x, dsignrank(x,n=n), type='l', main=paste("dsignrank(x,n=",n,")"))
}

[Package

*stats* version 2.2.1

Index]