SignRank {base}

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	numbers of observations in the sample. Must be positive integers less than 50.
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].

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.

Value

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

Author(s)

Kurt Hornik hornik@ci.tuwien.ac.at

See Also

dwilcox etc, for the 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,")"))
}

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