zeta                   package:sn                   R Documentation

_F_u_n_c_t_i_o_n `_l_o_g(_2*_P(_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 P(x))' and its derivatives up to order 4, if
     P(x) denotes the standard normal distribution function.

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

     zeta(k, x)

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

       k: an integer scalar. 

       x: a vector. Missing values (`NA's) are allowed, but `Inf's are
          not. 

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

     `k' denotes the order of the derivative. If `k' is 0, the function
     is evaluated, using `pnorm(x)' for `x>-35',  an asymptotic
     expansion otherwise. For `k' between 1 and 4, the derivative of
     that order is evaluated. For `k>4', a warning message is issued,
     and a vector of `NA's is returned.

     This function is used by `sn.dev' and `msn.dev', among others.

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

     a vector; this is 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(i in 0:4) 
           curve(zeta(i,x),-3, 4, ylim = c(-1,2), col = i+1, add = i > 0)

