studentt                package:VGAM                R Documentation

_S_t_u_d_e_n_t _t _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 the degrees of freedom for a Student t distribution.

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

     studentt(link.df = "loglog")

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

 link.df: Parameter link function for the degrees of freedom nu. See
          'Links' for more choices. The default ensures the parameter
          is greater than unity.

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

     The density function is

 f(y) = (gamma((nu+1)/2) / (sqrt(nu*pi) gamma(nu/2))) * (1 + y^2 / nu)^{-(nu+1)/2}

     for all real y. Then E(Y)=0 if nu>1 (returned as the fitted
     values), and Var(Y)= nu/(nu-2) for nu > 2. When nu=1 then the
     Student t-distribution  corresponds to the standard Cauchy
     distribution. The degrees of freedom is treated as a parameter to
     be estimated, and as real and not integer.

_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:

     A standard normal distribution corresponds to a _t_ distribution
     with infinite degrees of freedom.  Consequently, if the data is
     close to normal, there may be convergence problems.

_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.

     Student (1908) The probable error of a mean. _Biometrika_, *6*,
     1-25.

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

     'normal1', 'loglog', 'TDist'.

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

     n = 200
     y = rt(n, df=exp(2))
     fit = vglm(y ~ 1, studentt)
     coef(fit, matrix=TRUE)
     Coef(fit) 

