fgm                   package:VGAM                   R Documentation

_F_a_r_l_i_e-_G_u_m_b_e_l-_M_o_r_g_e_n_s_t_e_r_n'_s _B_i_v_a_r_i_a_t_e _D_i_s_t_r_i_b_u_t_i_o_n _F_a_m_i_l_y _F_u_n_c_t_i_o_n

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

     Estimate the association parameter of  Farlie-Gumbel-Morgenstern's
     bivariate distribution using maximum likelihood estimation.

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

     fgm(lapar="identity", earg=list(), iapar=NULL, method.init=1)

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

   lapar: Link function applied to the association parameter alpha,
          which is real. See 'Links' for more choices.

    earg: List. Extra argument for the link. See 'earg' in 'Links' for
          general information.

   iapar: Numeric. Optional initial value for alpha. By default, an
          initial value is chosen internally. If a convergence failure
          occurs try assigning a different value. Assigning a value
          will override the argument 'method.init'.

method.init: An integer with value '1' or '2' which specifies the
          initialization method. If failure to converge occurs try the
          other value, or else specify a value for 'ia'.

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

     The cumulative distribution function is

 P(Y1 <= y1, Y2 <= y2) =  y1 * y2 * ( 1 + alpha * (1 - y1) * (1 - y2) )

     for real alpha (the range is data-dependent). The support of the
     function is the unit square. The marginal distributions are the
     standard uniform distributions. When alpha=0 then the random
     variables are independent.

     A variant of Newton-Raphson is used, which only seems to work for
     an intercept model. It is a very good idea to set 'trace=TRUE'.
     This 'VGAM' family function is prone to numerical difficulties.

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

     An object of class '"vglmff"' (see 'vglmff-class'). The object is
     used by modelling functions such as 'vglm' and 'vgam'.

_N_o_t_e:

     The response must be a two-column matrix.  Currently, the fitted
     value is a matrix with two columns and values equal to 0.5. This
     is because each marginal distribution corresponds to a standard
     uniform distribution.

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

     T. W. Yee

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

     Castillo, E., Hadi, A. S., Balakrishnan, N. Sarabia, J. S. (2005)
     _Extreme Value and Related Models with Applications in Engineering
     and Science_, Hoboken, N.J.: Wiley-Interscience.

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

     'frank', 'morgenstern'.

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

     n = 1000
     ymat = cbind(runif(n), runif(n))
     ## Not run: plot(ymat)
     fit = vglm(ymat ~ 1, fam=fgm, trace=TRUE)
     fit = vglm(ymat ~ 1, fam=fgm, trace=TRUE, crit="coef")
     coef(fit, matrix=TRUE)
     Coef(fit)
     fitted(fit)[1:5,]

