wald                  package:VGAM                  R Documentation

_W_a_l_d _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:

     Estimates the parameter of the standard Wald distribution by
     maximum likelihood estimation.

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

     wald(link.lambda="loge", earg=list(), init.lambda=NULL)

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

link.lambda: Parameter link function for the lambda parameter.  See
          'Links' for more choices.

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

init.lambda: Initial value for the lambda parameter. The default means
          an initial value is chosen internally.

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

     The standard Wald distribution is a special case of the inverse
     Gaussian distribution with mu=1. It has a density that can be
     written as

 f(y;mu,lambda) = sqrt(lambda/(2*pi*y^3)) * exp(-lambda*(y-1)^2/(2*y))

     where y>0 and lambda>0. The mean of Y is 1 (returned as the fitted
     values) and its variance is 1/lambda. By default, eta=log(lambda).

_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 'VGAM' family function 'inv.gaussianff' estimates the location
     parameter mu too.

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

     T. W. Yee

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

     Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994)
     _Continuous Univariate Distributions_, 2nd edition, Volume 1, New
     York: Wiley.

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

     'inv.gaussianff'.

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

     set.seed(123)
     shape = 1
     y = rgamma(n=1000, shape=shape) # Not inverse Gaussian!!
     fit = vglm(y ~ 1, wald(init=0.2), trace=TRUE)
     coef(fit, matrix=TRUE)
     Coef(fit)
     summary(fit)

