dagum                  package:VGAM                  R Documentation

_D_a_g_u_m _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 3-parameter  Dagum
     distribution.

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

     dagum(link.a = "loge", link.scale = "loge", link.p = "loge",
           earg.a=list(), earg.scale=list(), earg.p=list(),
           init.a = NULL, init.scale = NULL, init.p = 1, zero = NULL)

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

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

earg.a, earg.scale, earg.p: List. Extra argument for each of the links.
          See 'earg' in 'Links' for general information.

init.a, init.scale, init.p: Optional initial values for 'a', '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 {1,2,3} which correspond to 'a',
          'scale', 'p', respectively.

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

     The 3-parameter Dagum distribution is the 4-parameter generalized
     beta II distribution with shape parameter q=1. It is known under
     various other names, such as the Burr III, inverse Burr, beta-K,
     and 3-parameter kappa distribution. It can be considered a
     generalized log-logistic distribution. Some distributions which
     are special cases of the 3-parameter Dagum are the inverse Lomax
     (a=1), Fisk (p=1), and the inverse paralogistic (a=p). More
     details can be found in Kleiber and Kotz (2003).

     The Dagum distribution has a cumulative distribution function

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

     which leads to a probability density function

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

     for a > 0, b > 0, p > 0, y > 0. Here, b is the scale parameter
     'scale', and the others are shape parameters. The mean is

         E(Y) = b  gamma(p + 1/a)  gamma(1 - 1/a) /  gamma(p)

     provided -ap < 1 < a.

_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'.

     From Kleiber and Kotz (2003), the MLE is rather sensitive to
     isolated observations located sufficiently far from the majority
     of the data. Reliable estimation of the scale parameter require
     n>7000, while estimates for a and p can be considered unbiased for
     n>2000 or 3000.

_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:

     'Dagum', 'genbetaII', 'betaII', 'sinmad', 'fisk', 'invlomax',
     'lomax', 'paralogistic', 'invparalogistic'.

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

     y = rdagum(n=3000, 4, 6, 2)
     fit = vglm(y ~ 1, dagum, trace=TRUE)
     fit = vglm(y ~ 1, dagum(init.a=2.1), trace=TRUE, crit="c")
     coef(fit, mat=TRUE)
     Coef(fit)
     summary(fit)

