cauchy1                 package:VGAM                 R Documentation

_C_a_u_c_h_y _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:

     Estimates the location parameter of the Cauchy distribution by
     maximum likelihood estimation.

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

     cauchy1(scale.arg=1, llocation="identity",
             elocation=list(), ilocation=NULL, method.init=1)

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

scale.arg: Known (positive) scale parameter, called s below. 

llocation: Parameter link function for the a location parameter. See
          'Links' for more choices.

elocation: List. Extra argument for the link. See 'earg' in 'Links' for
          general information.

ilocation: Optional initial value for a. By default, an initial value
          is chosen internally. 

method.init: Integer, either 1 or 2 or 3. Initial method, three
          algorithms are implemented. Choose the another value if
          convergence fails, or use 'ilocation'.

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

     The Cauchy distribution has a density function 

             f(y;a,s) = 1 / [pi * s * [1 + ((y-a)/s)^2]]

     where y and a are real and finite, and s>0. The distribution is
     symmetric about a and has a heavy tail. Its median and mode are a,
     but the mean does not exist, therefore the fitted values are all
     'NA's. Fisher scoring is used.

_V_a_l_u_e:

     An object of class '"vglmff"' (see 'vglmff-class'). The object is
     used by modelling functions such as 'vglm', 'rrvglm' and 'vgam'.

_N_o_t_e:

     Good initial values are needed. It pays to select a wide range of
     initial values via the 'ilocation' and 'method.init' arguments.

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

     T. W. Yee

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

     Evans, M., Hastings, N. and Peacock, B. (2000) _Statistical
     Distributions_, New York: Wiley-Interscience, Third edition.

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

     'Cauchy', 'cauchit'.

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

     set.seed(123)
     n = 500
     x = runif(n)

     y = rcauchy(n, loc=1+5*x, scale=.4)
     fit = vglm(y ~ x, cauchy1(scale=0.4), trace =TRUE, crit="c")
     coef(fit, matrix=TRUE)

     y = rcauchy(n, loc=exp(1+0.5*x), scale=.4)
     ## Not run: hist(y)
     fit = vglm(y ~ x, cauchy1(scale=0.4, lloc="loge"), trace=TRUE, crit="c")
     coef(fit, matrix=TRUE)
     fitted(fit)[1:4]
     summary(fit)

