genpoisson               package:VGAM               R Documentation

_G_e_n_e_r_a_l_i_z_e_d _P_o_i_s_s_o_n _d_i_s_t_r_i_b_u_t_i_o_n

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

     Estimation of the two parameters of a generalized Poisson
     distribution.

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

     genpoisson(llambda = "logit", ltheta = "loge",
                ilambda = 0.5, itheta = NULL, zero = NULL)

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

 llambda: Parameter link function for 'lambda'. See 'Links' for more
          choices. The parameter lies in the unit interval, therefore
          the logit link is a reasonable default.

  ltheta: Parameter link function for 'theta'.  See 'Links' for more
          choices. The parameter is positive, therefore the default is
          the log link. 

 ilambda: Optional initial value for 'lambda'. 

  itheta: Optional initial value for 'theta'. 

    zero: An integer vector, containing the value 1 or 2. If so,
          'lambda' or 'theta' respectively are modelled as an intercept
          only. The default value 'NULL' means both linear/additive
          predictors are modelled as functions of the explanatory
          variables. 

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

     See Consul (1989) for details.

_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:

     Convergence problems may occur when 'lambda' is very close to 0. 
     This distribution is useful for dispersion modelling.

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

     T. W. Yee

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

     Jorgensen, B. (1997) _The Theory of Dispersion Models_. London:
     Chapman & Hall

     Consul, P. C. (1989) _Generalized Poisson Distributions:
     Properties and Applications_, Marcel Dekker.

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

     'poissonff'.

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

     y = rpois(n=100, lam=24)
     fit  = vglm(y ~ 1, genpoisson, trace=TRUE)
     fitted(fit)[1:5]
     mean(y)
     summary(fit)
     coef(fit, matrix=TRUE)
     Coef(fit)

