

SignRank {base}                              R Documentation

_D_i_s_t_r_i_b_u_t_i_o_n _o_f _t_h_e _W_i_l_c_o_x_o_n _S_i_g_n_e_d _R_a_n_k _S_t_a_t_i_s_t_i_c

_U_s_a_g_e_:

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

_A_r_g_u_m_e_n_t_s_:

     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.

_V_a_l_u_e_:

     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.

_A_u_t_h_o_r_(_s_)_:

     Kurt Hornik hornik@ci.tuwien.ac.at

_S_e_e _A_l_s_o_:

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

_E_x_a_m_p_l_e_s_:

     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,")"))
     }

