Frank                  package:VGAM                  R Documentation

_F_r_a_n_k'_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, quantile function and random
     generation for the one parameter Frank distribution.

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

     dfrank(x1, x2, alpha)
     pfrank(q1, q2, alpha)
     rfrank(n, alpha)

_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.

   alpha: the positive association parameter alpha.

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

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

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

     'dfrank' gives the density, 'pfrank' gives the distribution
     function, and 'rfrank' 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:

     Genest, C. (1987) Frank's family of bivariate distributions.
     _Biometrika_, *74*, 549-555.

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

     'frank'.

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

     ## Not run: 
     N = 100
     x = seq(-0.30, 1.30, len=N)
     alpha = 8
     ox = expand.grid(x, x)
     z = dfrank(ox[,1], ox[,2], alp=alpha)
     contour(x, x, matrix(z, N, N))
     z = pfrank(ox[,1], ox[,2], alp=alpha)
     contour(x, x, matrix(z, N, N))

     alpha = exp(4)
     plot(r <- rfrank(n=3000, alpha=alpha))
     par(mfrow=c(1,2))
     hist(r[,1]) # Should be uniform
     hist(r[,2]) # Should be uniform
     ## End(Not run)

