bilogis4                package:VGAM                R Documentation

_B_i_v_a_r_i_a_t_e _L_o_g_i_s_t_i_c _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 4-parameter bivariate logistic distribution.

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

     dbilogis4(x1, x2, loc1=0, scale1=1, loc2=0, scale2=1)
     pbilogis4(q1, q2, loc1=0, scale1=1, loc2=0, scale2=1)
     rbilogis4(n, loc1=0, scale1=1, loc2=0, scale2=1)

_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.

loc1, loc2: the location parameters l1 and l2.

scale1, scale2: the scale parameters s1 and s2.

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

     See 'bilogis4', the 'VGAM' family function for estimating the four
     parameters by maximum likelihood estimation, for the formula of
     the cumulative distribution function and other details.

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

     'dbilogis4' gives the density, 'pbilogis4' gives the distribution
     function, and 'rbilogis4' 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:

     Gumbel, E. J. (1961) Bivariate logistic distributions. _Journal of
     the American Statistical Association_, *56*, 335-349.

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

     'bilogistic4'.

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

     ## Not run: 
     par(mfrow=c(1,3))
     n = 2000
     ymat = rbilogis4(n, loc1=5, loc2=7, scale2=exp(1))
     myxlim = c(-2,15)
     myylim = c(-10,30)
     plot(ymat, xlim=myxlim, ylim=myylim)

     N = 100
     x1 = seq(myxlim[1], myxlim[2], len=N)
     x2 = seq(myylim[1], myylim[2], len=N)
     ox = expand.grid(x1, x2)
     z = dbilogis4(ox[,1], ox[,2], loc1=5, loc2=7, scale2=exp(1))
     contour(x1, x2, matrix(z, N, N), main="density")
     z = pbilogis4(ox[,1], ox[,2], loc1=5, loc2=7, scale2=exp(1))
     contour(x1, x2, matrix(z, N, N), main="cdf")
     ## End(Not run)

