zeta                   package:sn                   R Documentation

_F_u_n_c_t_i_o_n `_l_o_g(_2*_p_n_o_r_m(_x))' _a_n_d _i_t_s _d_e_r_i_v_a_t_i_v_e_s

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

     The function `log(2*(pnorm(x))' and its derivatives up to order 4.

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

     zeta(k, x)

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

       k: an integer scalar between 0 and 4. 

       x: a vector. Missing values (`NA's)  and `Inf's are allowed 

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

     For `k' between 0 and 4, the derivative of  order `k' of
     `log(2*pnorm(x))' is  evaluated, where the derivative of order
     `k=0' refers to  the function itself. If `k' is not integer, it is
     converted to integer and a warning message is generated. If `k<0'
     or `k>4',  `NULL' is returned. This function is used by `sn.dev'
     and `msn.dev', among others.

_V_a_l_u_e:

     a vector giving the `k'-th order derivative evaluated at `x'

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

     `sn.mle', `msn.mle'

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

     y <- zeta(2,seq(-20,20,by=0.5))
     #
     for(k in 0:4) curve(zeta(k,x), from=-1, to=5, col = k+2, add = k > 0)
     legend(3, -0.5, legend=as.character(0:4), col=2:6, lty=1)

