stats (version 3.6.2)

# SignRank: 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 \(P[X \le x]\), otherwise, \(P[X > x]\).

## Value

`dsignrank` gives the density, `psignrank` gives the distribution function, `qsignrank` gives the quantile function, and `rsignrank` generates random deviates.

The length of the result is determined by `nn` for `rsignrank`, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than `nn` are recycled to the length of the result. Only the first elements of the logical arguments are used.

## 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.

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

Distributions for standard distributions, including `dwilcox` for the distribution of two-sample Wilcoxon rank sum statistic.

## Examples

Run this code
``````# NOT RUN {
require(graphics)

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 = paste0("dsignrank(x, n = ", n, ")"))
}
# }
``````

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