pospoisson               package:VGAM               R Documentation

_P_o_s_i_t_i_v_e _P_o_i_s_s_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:

     Fits a positive Poisson distribution.

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

     pospoisson(link = "loge")

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

    link: Link function for the usual mean (lambda) parameter of an
          ordinary Poisson distribution. See 'Links' for more choices.

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

     The positive Poisson  distribution is the ordinary Poisson
     distribution but with the probability of zero being zero.  Thus
     the other probabilities are scaled up (i.e., divided by 1-P[Y=0]).
     The mean, lambda/(1-exp(-lambda)), can be obtained by the
     extractor function 'fitted' applied to the object.

     A related distribution is the zero-inflated Poisson, in which the
     probability P[Y=0] involves another parameter phi. See
     'zipoisson'.

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

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

_W_a_r_n_i_n_g:

     Under- or over-flow may occur if the data is ill-conditioned.

_N_o_t_e:

     Yet to be done: a 'quasi.pospoisson' which estimates a dispersion
     parameter.

     This family function can handle a multivariate response.

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

     Thomas W. Yee

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

     Coleman, J. S. and James, J. (1961) The equilibrium size
     distribution of freely-forming groups. _Sociometry_, *24*, 36-45.

     Documentation accompanying the 'VGAM' package at <URL:
     http://www.stat.auckland.ac.nz/~yee> contains further information
     and examples.

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

     'Pospois', 'posnegbinomial', 'poissonff', 'zipoisson'.

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

     y = 1:6
     w = c(1486, 694, 195, 37, 10, 1) # Data from Coleman and James (1961)
     fit = vglm(y ~ 1, pospoisson, weights=w)
     Coef(fit)
     summary(fit)
     fitted(fit)

     # Artificial data
     x = runif(n <- 1000)
     lambda = exp(2 + 3*x)
     y = rpospois(n, lambda)
     table(y)
     fit = vglm(y ~ x, pospoisson, trace=TRUE, crit="c")
     coef(fit, matrix=TRUE)

