

   DDiissttrriibbuuttiioonn ooff tthhee WWiillccooxxoonn SSiiggnneedd RRaannkk SSttaattiissttiicc

        dsignrank(x, n)
        psignrank(q, n)
        qsignrank(p, n)
        rsignrank(nn, n)

   AArrgguummeennttss::

        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.

   VVaalluuee::

        These functions provide information about the distribu-
        tion 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 `rsign-
        rank' generates random deviates.

        This distribution is obtained as follows.  Let `x' be a
        sample of size `n' from a continuous distribution sym-
        metric about the origin.  Then the Wilcoxon signed rank
        statistic is the sum of the ranks of the absolute val-
        ues `x[i]' for which `x[i]' is positive.  This statis-
        tic 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, respec-
        tively.

   AAuutthhoorr((ss))::

        Kurt Hornik hornik@ci.tuwien.ac.at

   SSeeee AAllssoo::

        `dwilcox' etc, for the two-sample Wilcoxon rank sum
        statistic.

   EExxaammpplleess::

        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,")"))
        }

