gamma1                 package:VGAM                 R Documentation

_1-_p_a_r_a_m_e_t_e_r _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:

     Estimates the 1-parameter gamma distribution by maximum likelihood
     estimation.

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

     gamma1(link = "loge", earg=list())

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

    link: Link function applied to the (positive) _shape_ parameter.
          See 'Links' for more choices.

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

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

     The density function is given by

              f(y) = exp(-y) y^(shape-1) / gamma(shape)

     for shape > 0 and y > 0. Here, gamma(shape) is the gamma function,
     as in 'gamma'. The mean of Y (returned as the fitted values) is
     mu=shape, and the variance is  sigma^2 = shape.

_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:

     This 'VGAM' family function can handle a multivariate (matrix)
     response.

     The parameter shape matches with 'shape' in 'rgamma'. The argument
     'rate' in 'rgamma' is assumed 1 for this family function.

     If rate is unknown use the family function 'gamma2.ab' to estimate
     it too.

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

     T. W. Yee

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

     Most standard texts on statistical distributions describe the
     1-parameter gamma distribution, e.g.,

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

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

     'gamma2.ab' for the 2-parameter gamma distribution.

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

     y = rgamma(n=100, shape= exp(3))
     fit = vglm(y ~ 1, gamma1, trace=TRUE, crit="c")
     coef(fit, matrix=TRUE)
     Coef(fit)
     summary(fit)

