Plackett                package:VGAM                R Documentation

_P_l_a_c_k_e_t_t'_s _B_i_v_a_r_i_a_t_e _D_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Density, distribution function, and random generation for the (one
     parameter) bivariate Plackett distribution.

_U_s_a_g_e:

     dplack(x1, x2, oratio, log=FALSE)
     pplack(q1, q2, oratio)
     rplack(n, oratio)

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

x1, x2, q1, q2: vector of quantiles.

       n: number of observations. Must be a positive integer of length
          1.

  oratio: the positive odds ratio psi.

     log: Logical. If 'TRUE' then the logarithm is returned.

_D_e_t_a_i_l_s:

     See 'plackett', the 'VGAM' family functions for estimating the
     parameter by maximum likelihood estimation, for the formula of the
     cumulative distribution function and other details.

_V_a_l_u_e:

     'dplack' gives the density, 'pplack' gives the distribution
     function, and 'rplack' generates random deviates (a two-column
     matrix).

_A_u_t_h_o_r(_s):

     T. W. Yee

_R_e_f_e_r_e_n_c_e_s:

     Mardia, K. V. (1967) Some contributions to contingency-type
     distributions. _Biometrika_, *54*, 235-249.

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

     'plackett', 'frank'.

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

     ## Not run: 
     N = 101
     x = seq(0.0, 1.0, len=N)
     oratio = exp(1)
     ox = expand.grid(x, x)
     z = dplack(ox[,1], ox[,2], oratio=oratio)
     contour(x, x, matrix(z, N, N), col="blue")
     z = pplack(ox[,1], ox[,2], oratio=oratio)
     contour(x, x, matrix(z, N, N), col="blue")

     plot(r <- rplack(n=3000, oratio=oratio))
     par(mfrow=c(1,2))
     hist(r[,1]) # Should be uniform
     hist(r[,2]) # Should be uniform
     ## End(Not run)

