fff                   package:VGAM                   R Documentation

_F _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) F distribution.

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

     fff(link="loge", idf1=NULL, idf2=NULL, method.init=1, zero=NULL)

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

    link: Parameter link function for both parameters. See 'Links' for
          more choices. The default keeps the parameters positive.

idf1,idf2: Numeric and positive.  Initial value for the parameters. The
          default is to choose each value internally.

method.init: Initialization method. Either the value 1 or 2. If both
          fail try setting values for 'idf1' and 'idf2'.

    zero: An integer-valued vector specifying which linear/additive
          predictors are modelled as intercepts only. The value must be
          from the set {1,2}, corresponding respectively to df1 and
          df2. By default all linear/additive predictors are modelled
          as a linear combination of the explanatory variables.

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

     The F distribution is named after Fisher and has a density
     function  that has two parameters, called 'df1' and 'df2' here.
     This function treats these degrees of freedom as _positive reals_
     rather than integers.  The mean of the distribution is df2/(df2-2)
     provided df2>2, and its variance is 2*df2^2*(df1+df2-2)/
     (df1*(df2-2)^2*(df2-4)) provided df2>4. The estimated mean is
     returned as the fitted values. Although the F distribution can be
     defined to accommodate a non-centrality parameter 'ncp', it is
     assumed zero here.

_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'.

_W_a_r_n_i_n_g:

     Numerical problems will occur when the estimates of the parameters
     are too low.

_N_o_t_e:

     This family function uses the BFGS quasi-Newton update formula for
     the working weight matrices.  Consequently the estimated
     variance-covariance matrix may be inaccurate or simply wrong! The
     standard errors must be therefore treated with caution; these are
     computed in functions such as 'vcov()' and 'summary()'.

_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:

     'FDist'.

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

     x = runif(n <- 4000)
     df1 = exp(2+0.5*x)
     df2 = exp(2-0.5*x)
     y = rf(n, df1, df2)
     fit = vglm(y  ~ x, fff, trace=TRUE)
     coef(fit, matrix=TRUE)
     Coef(fit)
     vcov(fit)   # caution needed!

