SignRank                package: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 <= 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,")"))
     }

