amh                   package:VGAM                   R Documentation

_A_l_i-_M_i_k_h_a_i_l-_H_a_q _D_i_s_t_r_i_b_u_t_i_o_n _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 Ali-Mikhail-Haq's bivariate
     distribution by maximum likelihood estimation.

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

     amh(lalpha="rhobit", ealpha=list(), ialpha=NULL,
         method.init=1, nsimEIM=250)

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

  lalpha: Link function applied to the association parameter alpha,
          which is real and -1 < alpha < 1. See 'Links' for more
          choices.

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

  ialpha: 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 'ialpha'.

 nsimEIM: See 'CommonVGAMffArguments' for more information.

_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 -1 < alpha < 1. The support of the function is the unit
     square. The marginal distributions are the standard uniform
     distributions. When alpha=0 the random variables are independent.

_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 and C. S. Chee

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

     Hutchinson, T. P. and Lai, C. D. (1990) _Continuous Bivariate
     Distributions, Emphasising Applications_, Adelaide, South
     Australia: Rumsby Scientific Publishing.

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

     'ramh', 'fgm', 'gumbelIbiv'.

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

     ymat = ramh(1000, alpha=rhobit(2, inverse=TRUE))
     fit = vglm(ymat ~ 1, amh, trace = TRUE)
     coef(fit, mat=TRUE)
     Coef(fit)

