normal1                 package:VGAM                 R Documentation

_U_n_i_v_a_r_i_a_t_e _n_o_r_m_a_l _d_i_s_t_r_i_b_u_t_i_o_n

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

     Maximum likelihood estimation of the two parameters of a
     univariate normal distribution.

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

     normal1(lmean="identity", lsd="loge", zero=NULL)

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

   lmean: Link function applied to the mean. See 'Links' for more
          choices.

     lsd: Parameter link function applied to the standard deviation.
          See 'Links' for more choices. Being a positive quantity, a
          log link is the default.

    zero: An integer vector, containing the value 1 or 2. If so, the
          mean or standard deviation respectively are modelled as an
          intercept only. Usually, setting 'zero=2' will be used, if
          used at all. The default value 'NULL' means both
          linear/additive predictors are modelled as functions of the
          explanatory variables.

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

     By default, the mean is the first linear/additive predictor and 
     the log of the standard deviation is the second linear/additive
     predictor. The Fisher information matrix is diagonal.

_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:

     The response should be univariate. Multivariate responses are more
     generally handled using 'gaussianff', however this only handles
     the mean and the variance-covariance matrices are assumed known.

_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:

     'gaussianff', 'posnormal1', 'tobit', 'cnormal1', 'dcnormal1',
     'studentt'.

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

     n = 200
     x = rnorm(n)
     y = rnorm(n, mean=1-3*x, sd=exp(1+0.2*x))
     fit = vglm(y ~ x, normal1)
     coef(fit, matrix=TRUE)

     # Generate a random sample from a N(mu=theta, sigma=theta)
     # distribution with theta=10. Then estimate theta.
     theta = 10
     y = rnorm(100, m=theta, sd=theta)
     fit = vglm(y ~ 1, normal1(lsd="identity"),
                constraints=list("(Intercept)"=rbind(1,1)))
     coef(fit, matrix=TRUE)

