invlomax                package:VGAM                R Documentation

_I_n_v_e_r_s_e _L_o_m_a_x _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:

     Maximum likelihood estimation of the 2-parameter  inverse Lomax
     distribution.

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

     invlomax(link.scale = "loge", link.p = "loge",
              init.scale = NULL, init.p = 1, zero = NULL)

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

link.scale, link.p: Parameter link functions applied to the (positive)
          scale parameter 'scale' and (positive) shape parameter 'p'.
          See 'Links' for more choices.

init.scale, init.p: Optional initial values for 'scale' and 'p'.

    zero: An integer-valued vector specifying which linear/additive
          predictors are modelled as intercepts only. Here, the values
          must be from the set {1,2} which correspond to 'scale', 'p',
          respectively.

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

     The 2-parameter inverse Lomax distribution is the 4-parameter
     generalized beta II distribution with shape parameters a=q=1. It
     is also the 3-parameter Dagum distribution with shape parameter
     a=1, as well as the beta distribution of the second kind with q=1.
     More details can be found in Kleiber and Kotz (2003).

     The inverse Lomax distribution has density

               f(y) = p y^(p-1) / [b^p (1 + y/b)^(p+1)]

     for b > 0, p > 0, y > 0. Here, b is the scale parameter 'scale',
     and 'p' is a shape parameter. The mean does not seem to exist.

_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:

     If the self-starting initial values fail, try experimenting with
     the initial value arguments, especially those whose default value
     is not 'NULL'.

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

     T. W. Yee

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

     Kleiber, C. and Kotz, S. (2003) _Statistical Size Distributions in
     Economics and Actuarial Sciences_, Hoboken, NJ:
     Wiley-Interscience.

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

     'Invlomax', 'genbetaII', 'betaII', 'dagum', 'sinmad', 'fisk',
     'lomax', 'paralogistic', 'invparalogistic'.

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

     y = rinvlomax(n=2000, 6, 2)
     fit = vglm(y ~ 1, invlomax, trace=TRUE)
     fit = vglm(y ~ 1, invlomax, trace=TRUE, crit="c")
     coef(fit, mat=TRUE)
     Coef(fit)
     summary(fit)

