| SignRank {base} | R Documentation |
Distribution of the Wilcoxon Signed Rank Statistic
Usage
dsignrank(x, n)
psignrank(q, n)
qsignrank(p, n)
rsignrank(nn, n)
Arguments
x, q |
vector of quantiles. |
p |
vector of probabilities. |
nn |
number of observations to generate. |
n |
numbers of observations in the sample. Must be positive integers less than 50. |
Value
These functions provide information about the distribution of the
Wilcoxon Signed Rank statistic obtained from a sample with size
n. dsignrank gives the density, psignrank
gives the distribution function, qsignrank gives the quantile
function, and rsignrank generates random deviates.
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.
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,")"))
}