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)

