prentice74               package:VGAM               R Documentation

_P_r_e_n_t_i_c_e (_1_9_7_4) _L_o_g-_g_a_m_m_a _D_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Estimation of a 3-parameter log-gamma distribution described by
     Prentice (1974).

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

     prentice74(llocation="identity", lscale="loge", lshape="identity",
                ilocation=NULL, iscale=NULL, ishape=NULL, zero=NULL)

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

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

  lscale: Parameter link function applied to the positive scale
          parameter b. See 'Links' for more choices.

  lshape: Parameter link function applied to  the shape parameter q. 
          See 'Links' for more choices.

ilocation, iscale: Initial value for a and b, respectively. The
          defaults mean an initial value is determined internally for
          each.

  ishape: Initial value for q. If failure to converge occurs, try some
          other value. The default means an initial value is determined
          internally.

    zero: An integer-valued vector specifying which linear/additive
          predictors are modelled as intercepts only. The values must
          be from the set {1,2,3}. The default value means none are
          modelled as intercept-only terms.

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

     The probability density function is given by

       f(y;a,b,q) = |q| * exp(w/q^2 - e^w) / (b*gamma(1/q^2)),

     for shape parameter q != 0, positive scale parameter b > 0,
     location parameter a, and all real y. Here, w =
     (y-a)*q/b+psi(1/q^2) where psi is the digamma function. The mean
     of Y is a (returned as the fitted values). This is a different
     parameterization compared to 'lgamma3ff'.

     Special cases:  q=0 is the normal distribution with standard
     deviation b, q=-1 is the extreme value distribution for maxima,
     q=1 is the extreme value distribution for minima (Weibull). If q>0
     then the distribution is left skew, else q<0 is right skew.

_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:

     The special case q=0 is not handled, therefore estimates of q too
     close to zero may cause numerical problems.

_N_o_t_e:

     The notation used here differs from Prentice (1974): alpha=a,
     sigma=b. Fisher scoring is used.

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

     T. W. Yee

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

     Prentice, R. L. (1974) A log gamma model and its maximum
     likelihood estimation. _Biometrika_, *61*, 539-544.

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

     'lgamma3ff', 'lgamma'.

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

     x = runif(n <- 5000)
     loc = -1 + 2*x
     Scale = exp(1+x)
     y = rlgamma(n, loc=loc, scale=Scale, k=1)
     fit = vglm(y ~ x, prentice74(zero=3), trace=TRUE)
     coef(fit, matrix=TRUE)  # Note the coefficients for location

