fisk                  package:VGAM                  R Documentation

_F_i_s_k _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  Fisk
     distribution.

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

     fisk(link.a = "loge", link.scale = "loge",
          earg.a=list(), earg.scale=list(),
          init.a = NULL, init.scale = NULL, zero = NULL)

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

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

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

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

    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 'a', 'scale',
          respectively.

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

     The 2-parameter Fisk (aka log-logistic) distribution is the
     4-parameter generalized beta II distribution with shape parameter
     q=p=1. It is also the 3-parameter Singh-Maddala distribution with
     shape parameter q=1, as well as the  Dagum distribution with p=1.
     More details can be found in Kleiber and Kotz (2003).

     The Fisk distribution has density

               f(y) = a y^(a-1) / [b^a (1 + (y/b)^a)^2]

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

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

     The mean is

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

     provided a > 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:

     'Fisk', 'genbetaII', 'betaII', 'dagum', 'sinmad', 'invlomax',
     'lomax', 'paralogistic', 'invparalogistic'.

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

     y = rfisk(n=200, 4, 6)
     fit = vglm(y ~ 1, fisk, trace=TRUE)
     fit = vglm(y ~ 1, fisk(init.a=3.3), trace=TRUE, crit="c")
     coef(fit, mat=TRUE)
     Coef(fit)
     summary(fit)

