lomax                  package:VGAM                  R Documentation

_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  Lomax
     distribution.

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

     lomax(link.scale = "loge", link.q = "loge",
           init.scale = NULL, init.q = 1, zero = NULL)

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

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

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

    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', 'q',
          respectively.

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

     The 2-parameter Lomax distribution is the 4-parameter generalized
     beta II distribution with shape parameters a=p=1. It is probably
     more widely known as the Pareto (II) distribution. It is also the
     3-parameter Singh-Maddala distribution with shape parameter a=1,
     as well as the beta distribution of the second kind with p=1. More
     details can be found in Kleiber and Kotz (2003).

     The Lomax distribution has density

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

     for b > 0, q > 0, y > 0. Here, b is the scale parameter 'scale',
     and 'q' is a shape parameter. The cumulative distribution function
     is

                     F(y) = 1 - [1 + (y/b)]^(-q).

     The mean is

                            E(Y) = b/(q-1)

     provided q > 1.

_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:

     'Lomax', 'genbetaII', 'betaII', 'dagum', 'sinmad', 'fisk',
     'invlomax', 'paralogistic', 'invparalogistic'.

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

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

