yulesimon                package:VGAM                R Documentation

_Y_u_l_e-_S_i_m_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:

     Estimating the parameter of the Yule-Simon distribution.

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

     yulesimon(link="loge", earg=list(), irho=NULL, nsimEIM=200)

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

link, earg: Link function and extra argument for the rho parameter. See
          'Links' for more choices and for general information.

    irho: Optional initial value for the (positive) parameter.  See
          'CommonVGAMffArguments' for more information. The default is
          to obtain an initial value internally. Use this argument if
          the default fails.

 nsimEIM: See 'CommonVGAMffArguments' for more information.

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

     The probability function is

                    f(y;rho) = rho*beta(y,rho+1),

     where the parameter rho>0 and y=1,2,.... The function 'dyules'
     computes this probability function. The mean of Y, which is
     returned as fitted values, is rho/(rho-1) provided rho > 1. The
     variance of Y is rho^2/((rho-1)^2 (rho-2)) provided rho > 2.

_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'.

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

     T. W. Yee

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

     Simon, H. A. (1955) On a class of skew distribution functions.
     _Biometrika_, *42*, 425-440.

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

     'ryules'.

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

     x = runif(n <- 1000)
     y = ryules(n, rho=exp(1.5-x))
     table(y)
     fit = vglm(y ~ x, yulesimon, trace=TRUE)
     coef(fit, matrix=TRUE)
     summary(fit)

